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%I #13 Apr 09 2022 08:49:24
%S 1,0,1,3,19,171,2044,30528,547390,11457237,274198402,7385438214,
%T 221099038597,7282925988615,261763288109884,10194190355448399,
%U 427609812103844122,19220373155515189149,921621193002227307943,46958377673245988620737
%N Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (3 * j + x).
%F a(n) = Sum_{k=0..floor(n/2)} 3^(n-2*k) * |Stirling1(n-k,k)|.
%t a[n_] := Sum[3^(n-2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* _Amiram Eldar_, Apr 09 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 3*j+x)))
%o (PARI) a(n) = sum(k=0, n\2, 3^(n-2*k)*abs(stirling(n-k, k, 1)));
%Y Cf. A353255, A353257, A353258.
%Y Cf. A353262.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 08 2022
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