A357939 a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k).
1, 0, 0, 1, 0, 1, 1, 1, 3, 2, 7, 7, 16, 26, 41, 92, 128, 317, 478, 1107, 1977, 4077, 8547, 16310, 37775, 71489, 170660, 339138, 795833, 1705058, 3876254, 8926023, 19888522, 48187837, 107726407, 267597455, 613509355, 1531527270, 3646775589, 9066267823
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[StirlingS2[k,n-2k],{k,0,Floor[n/2]}],{n,0,40}] (* Harvey P. Dale, Jul 22 2025 *) -
PARI
a(n) = sum(k=0, n\2, stirling(k, n-2*k, 2));
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/prod(j=1, k, 1-j*x^2)))
Formula
G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x^2).