A357931 a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n - 2*k,n - 3*k)|.
1, 1, 1, 1, 2, 4, 7, 13, 27, 57, 120, 262, 593, 1361, 3171, 7559, 18356, 45186, 112927, 286689, 737641, 1921639, 5070154, 13540352, 36566737, 99830013, 275459693, 767798853, 2160953618, 6139721116, 17604534427, 50924095081, 148570523479, 437071675997
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[Abs[StirlingS1[n-2k,n-3k]],{k,0,Floor[n/3]}],{n,0,40}] (* Harvey P. Dale, Nov 01 2023 *) -
PARI
a(n) = sum(k=0, n\3, abs(stirling(n-2*k, n-3*k, 1)));
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 1+j*x^2)))
Formula
G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (1 + j * x^2).