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A352802
Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j + 3 * x).
3
1, 0, 3, 3, 15, 45, 198, 972, 5652, 37881, 289548, 2492640, 23906475, 253012653, 2930556024, 36883817127, 501315357690, 7318715960511, 114224260779891, 1897913866979529, 33449523840512127, 623265596538965334, 12241892922194658510, 252793167644378784006
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 3^k * |Stirling1(n-k,k)|.
MATHEMATICA
a[n_] := Sum[3^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 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, j+3*x)))
(PARI) a(n) = sum(k=0, n\2, 3^k*abs(stirling(n-k, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 09 2022
STATUS
approved