A187652 Alternated binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).

1, 0, 10, 194, 5932, 237624, 11820780, 702992968, 48662470640, 3843811669088, 341207224961856, 33627579102171680, 3643463136559851440, 430456189350273371648, 55075003474909952394848, 7586546772496980353804704

Offset

0,3

Links

Table of n, a(n) for n=0..15.

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 = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = 0.11686978539934159049334861225275481804523808136863346883911376048... - Vaclav Kotesovec, Jul 05 2021

Maple

seq(sum((-1)^(n-k)*binomial(n, k)*abs(combinat[stirling1](2*k, k)), k=0..n), n=0..12);

Mathematica

Table[Sum[(-1)^(n - k)Binomial[n, k]Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]

Prog

(Maxima) makelist(sum((-1)^(n-k)*binomial(n, k)*abs(stirling1(2*k, k)), k, 0, n), n, 0, 12);

Crossrefs

Cf. A187646.

Sequence in context: A006436 A252974 A341503 * A361311 A007816 A365176

Adjacent sequences: A187649 A187650 A187651 * A187653 A187654 A187655

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved