A353255 - OEIS

%I #11 Apr 09 2022 08:49:41

%S 1,0,1,2,9,54,429,4252,50605,703388,11184597,200247446,3986363597,

%T 87343744490,2088739037209,54134344486296,1511446306795417,

%U 45227224242345336,1443916049346447913,48989635949583331658,1760229264304229244753,66770472164443344587550

%N Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j + x).

%F a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * |Stirling1(n-k,k)|.

%t 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 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 2*j+x)))

%o (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*abs(stirling(n-k, k, 1)));

%Y Cf. A353256, A353257, A353258.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Apr 08 2022