The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A063024 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A063024

Reversion of y - y^2 - y^3 - y^4 - y^5.
(history; published version)

#11 by R. J. Mathar at Thu Jul 05 15:02:06 EDT 2012

FORMULA

a(n)=sum(k=1..n-1, (sum(j=0..k, binomial(k,j)*sum(i=j..n-k+j-1, binomial(j,i-j)*binomial(k-j,n-3*(k-j)-i-1))))*binomial(n+k-1,n-1)/n, n>1. a(1)=1. [_Vladimir Kruchinin kru(AT)ie.tusur.ru, _, May 10 2011]

PROG

a(n):=if n<2 then n else sum((sum(binomial(k, j)*sum(binomial(j, i-j)*binomial(k-j, n-3*(k-j)-i-1), i, j, n-k+j-1), j, 0, k))*binomial(n+k-1, n-1), k, 1, n-1)/n; [_Vladimir Kruchinin kru(AT)ie.tusur.ru, _, May 10 2011]

Vec(serreverse(x-sum(j=2, 6, x^j))) /* show terms */ /* _Joerg Arndt, _, May 12 2011 */

STATUS

approved

editing

#10 by Russ Cox at Fri Mar 30 17:20:58 EDT 2012

AUTHOR

_Olivier Gerard (olivier.gerard(AT)gmail.com), Gérard_, Jul 05 2001.

Discussion

Fri Mar 30

17:20

OEIS Server: https://oeis.org/edit/global/117

#9 by Russ Cox at Sun Jul 10 18:23:02 EDT 2011

LINKS

<a href="/Sindx_index/Res.html#revert">Index entries for reversions of series</a>

Discussion

Sun Jul 10

18:23

OEIS Server: https://oeis.org/edit/global/78

#8 by Joerg Arndt at Thu May 12 12:16:48 EDT 2011

STATUS

proposed

approved

#7 by Joerg Arndt at Thu May 12 12:16:44 EDT 2011

PROG

(Pari)

x='x+O('x^66); /* that many terms */

Vec(serreverse(x-sum(j=2, 6, x^j))) /* show terms */ /* Joerg Arndt, May 12 2011 */

#6 by Vladimir Kruchinin at Tue May 10 10:07:38 EDT 2011

FORMULA

a(n)=sum(k=1..n-1, (sum(j=0..k, binomial(k,j)*sum(i=j..n-k+j-1, binomial(j,i-j)*binomial(k-j,n-3*(k-j)-i-1))))*binomial(n+k-1,n-1)/n, n>1. a(1)=1. [Vladimir Kruchinin kru(AT)ie.tusur.ru, May 10 2011]

PROG

(Maxima)

a(n):=if n<2 then n else sum((sum(binomial(k, j)*sum(binomial(j, i-j)*binomial(k-j, n-3*(k-j)-i-1), i, j, n-k+j-1), j, 0, k))*binomial(n+k-1, n-1), k, 1, n-1)/n; [Vladimir Kruchinin kru(AT)ie.tusur.ru, May 10 2011]

STATUS

approved

proposed

#5 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_Res.html#revert">Index entries for reversions of series</a>

KEYWORD

nonn,easy,new

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_Res.html#revert">Index entries for reversions of series</a>

KEYWORD

nonn,easy,new

#3 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,easy,new

AUTHOR

Olivier Gerard (ogerardolivier.gerard(AT)ext.jussieugmail.frcom), Jul 05 2001.

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^4 - y^5, {y, 0, 30}], x], x]

KEYWORD

nonn,easy,new