The On-Line Encyclopedia of Integer Sequences (OEIS)

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A115137

Second diagonal of triangle A113647 (called Y(2,1)).
(history; published version)

#10 by Joerg Arndt at Wed May 22 05:47:18 EDT 2013

STATUS

reviewed

approved

#9 by Bruno Berselli at Wed May 22 02:43:23 EDT 2013

STATUS

proposed

reviewed

#8 by Vincenzo Librandi at Tue May 21 01:34:04 EDT 2013

STATUS

editing

proposed

#7 by Vincenzo Librandi at Tue May 21 01:33:55 EDT 2013

LINKS

Vincenzo Librandi, <a href="/A115137/b115137.txt">Table of n, a(n) for n = 0..300</a>

STATUS

approved

editing

#6 by Joerg Arndt at Fri Oct 19 03:18:14 EDT 2012

STATUS

proposed

approved

#5 by Vaclav Kotesovec at Fri Oct 19 03:08:50 EDT 2012

STATUS

editing

proposed

#4 by Vaclav Kotesovec at Fri Oct 19 03:08:45 EDT 2012

FORMULA

Recurrence: (n-2)*(n+1)*a(n) = (7*n^2-19*n+14)*a(n-1) + 4*(n-1)*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(3*n+2)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

CoefficientList[Series[(1-2*x)*(2*(1-Sqrt[1-8*x])/(4*x)-1)/(1+x), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

STATUS

approved

editing

#3 by Charles R Greathouse IV at Fri Oct 12 14:40:25 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006

Wolfdieter Lang, Jan 13 2006

Discussion

Fri Oct 12

14:40

OEIS Server: https://oeis.org/edit/global/1838

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

FORMULA

a(n)= A113647(n, n), n>=1.

KEYWORD

nonn,easy,new

#1 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

NAME

Second diagonal of triangle A113647 (called Y(2,1)).

DATA

1, 1, 7, 41, 247, 1545, 9975, 66057, 446455, 3067913, 21372919, 150618121, 1071841271, 7691763721, 55600938999, 404488323081, 2959189475319, 21757613309961, 160691417776119, 1191577871450121, 8868160862158839

OFFSET

0,3

FORMULA

a(n)= b(n) - 2*b(n-1) with b(n):=A062992(n)= A064062(n+1), n>=1. a(0):=1.

G.f.: (1-2*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).

a(n)= A113647(n,n), n>=1.

EXAMPLE

41=a(3)= A062992(3) - 2*A062992(2) = 67 - 2*13.

KEYWORD

nonn,easy,new

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006

STATUS

approved