A034942 Binomial transform of A002054.

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

Offset

0,2

Links

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

László Németh, Tetrahedron trinomial coefficient transform, arXiv:1905.13475 [math.CO], 2019.

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