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A353255
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j + x).
4
1, 0, 1, 2, 9, 54, 429, 4252, 50605, 703388, 11184597, 200247446, 3986363597, 87343744490, 2088739037209, 54134344486296, 1511446306795417, 45227224242345336, 1443916049346447913, 48989635949583331658, 1760229264304229244753, 66770472164443344587550
OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * |Stirling1(n-k,k)|.
MATHEMATICA
a[n_] := Sum[2^(n-2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 09 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 2*j+x)))
(PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*abs(stirling(n-k, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 08 2022
STATUS
approved