A097342 a(n) = Sum_{k=0..floor(n/2)} Stirling2(n-k,k) * 3^k.

1, 0, 3, 3, 12, 30, 93, 300, 1038, 3810, 14781, 60375, 258807, 1160949, 5435652, 26502555, 134282406, 705720549, 3840542031, 21608662710, 125523530724, 751831408929, 4637611255422, 29428408797852, 191907975348210

Offset: 0

Author

Paul Barry, Aug 05 2004

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..647

Crossrefs

Cf. A024427, A097341.

Programs

Mathematica

Table[Sum[StirlingS2[n-k,k]3^k,{k,0,Floor[n/2]}],{n,0,30}] (* Harvey P. Dale, May 24 2012 *)

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, 3^k*x^(2*k)/prod(j=1, k, 1-j*x))) \\ Seiichi Manyama, Apr 09 2022

PARI

a(n) = sum(k=0, n\2, 3^k*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 09 2022

Formula

a(n)=sum{k=0..floor(n/2), sum{i=0..k, (-1)^(k+i)i^(n-k)/(i!(k-i)!)}3^k }

G.f.: Sum_{k>=0} 3^k * x^(2*k)/Product_{j=1..k} (1 - j * x). - Seiichi Manyama, Apr 09 2022