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A063024 revision #19

A063024

Reversion of y - y^2 - y^3 - y^4 - y^5.

0, 1, 1, 3, 11, 45, 196, 894, 4215, 20377, 100463, 503191, 2553291, 13097469, 67808104, 353851124, 1859313324, 9828998946, 52237988523, 278952216129, 1495976545546, 8053571710250, 43507491045810, 235784617161780

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..23.

Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.

Index entries for reversions of series

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, May 10 2011]

MATHEMATICA

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

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, May 10 2011 */

(PARI)

x='x+O('x^66);

gf=serreverse(x-sum(j=2, 6, x^j));

Vec(gf)

/* Joerg Arndt, May 12 2011 */

CROSSREFS

Sequence in context: A049166 A049172 A049155 * A217887 A151129 A151130

Adjacent sequences: A063021 A063022 A063023 * A063025 A063026 A063027

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard, Jul 05 2001

STATUS

proposed