A353257 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j - x).

1, 0, -1, -2, -7, -42, -341, -3452, -41835, -590452, -9511213, -172182182, -3460540075, -76455710870, -1841772619273, -48043721545240, -1349168210580087, -40581475067022120, -1301688751836211065, -44352720153871514858, -1599833618118922360175

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * 2^(n-2*k) * |Stirling1(n-k,k)|.

Mathematica

a[n_] := Sum[(-1)^k * 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, (-1)^k*2^(n-2*k)*abs(stirling(n-k, k, 1)));

Crossrefs

Cf. A353255, A353256, A353258.

Sequence in context: A131682 A366453 A345368 * A368449 A317349 A158840

Adjacent sequences: A353254 A353255 A353256 * A353258 A353259 A353260

Keyword

sign

Author

Seiichi Manyama, Apr 08 2022

Status

approved