A353260 Expansion of Sum_{k>=0} (-1)^k * x^(2*k)/Product_{j=1..k} (1 - j * x).

1, 0, -1, -1, 0, 2, 5, 8, 6, -18, -111, -377, -953, -1567, 964, 23411, 133702, 554185, 1801323, 3910514, -2415952, -92788743, -700128734, -3842587204, -17042883146, -57693979779, -86308109341, 779904767601, 10180307035351, 78523141206142, 481780714913151

Offset

0,6

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * Stirling2(n-k,k).

Mathematica

a[n_] := Sum[(-1)^k * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 09 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (-1)^k*x^(2*k)/prod(j=1, k, 1-j*x)))
(PARI) a(n) = sum(k=0, n\2, (-1)^k*stirling(n-k, k, 2));

Crossrefs

Cf. A097341, A097342, A171367, A353261.

Cf. A353253.

Sequence in context: A360809 A287013 A057929 * A154127 A250206 A138371

Adjacent sequences: A353257 A353258 A353259 * A353261 A353262 A353263

Keyword

sign

Author

Seiichi Manyama, Apr 09 2022

Status

approved