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A034942 Binomial transform of A002054. 2
1, 6, 32, 163, 813, 4013, 19703, 96477, 471811, 2306316, 11274066, 55128021, 269688723, 1320047550, 6465047880, 31682288305, 155354522955, 762235643450, 3742013092520, 18380748447345, 90334417334095, 444186621323945, 2185193308168959, 10755153057295603, 52958560495897573 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

Recurrence: (n+3)*(3*n+1)*a(n) = 3*(6*n^2+15*n+11)*a(n-1) - 5*(n-1)*(3*n+4)*a(n-2). - Vaclav Kotesovec, Oct 08 2012

a(n) ~ 4*5^(n+1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 08 2012

MATHEMATICA

Table[Sum[Binomial[n, k]*Binomial[2*k+3, k], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 08 2012 *)

PROG

(PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial(2*k+3, k)); \\ Joerg Arndt, May 04 2013

CROSSREFS

Sequence in context: A037530 A083320 A097139 * A046714 A129171 A082585

Adjacent sequences:  A034939 A034940 A034941 * A034943 A034944 A034945

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 15 10:57 EDT 2018. Contains 316222 sequences. (Running on oeis4.)