A187651 Alternated binomial partial sums of the central Stirling numbers of the second kind.

1, 0, 6, 71, 1380, 34854, 1092317, 40900215, 1781924888, 88569337730, 4946558473226, 306691008191732, 20903038895529727, 1553426761730508586, 125016067017985968931, 10831572432055401760624, 1005245087722396707881648

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*S(2*k,k).

a(n) ~ c * d^n * (n-1)!, where d = 4/(w*(2-w)) = 6.176554609483480358231680164... and c = exp(w^2/4 - 1) / (Pi * sqrt(2*w * (1-w))) = 0.17569156962762991098958896633434384684339835018075095823375851..., where w = -LambertW(-2*exp(-2))^2 = -A226775. - Vaclav Kotesovec, Mar 30 2018, updated Jul 07 2021

Maple

seq(add((-1)^(n-k)*binomial(n, k)*combinat[stirling2](2*k, k), k=0..n), n=0..20);

Mathematica

Table[Sum[(-1)^(n-k)Binomial[n, k] StirlingS2[2k, k], {k, 0, n}], {n, 0, 16}]

Prog

(Maxima) makelist(sum((-1)^(n-k) *binomial(n, k) *stirling2(2*k, k), k, 0, n), n, 0, 12);

Crossrefs

Cf. A187653.

Sequence in context: A145089 A218676 A127135 * A357141 A005981 A024272

Adjacent sequences: A187648 A187649 A187650 * A187652 A187653 A187654

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved