A187654 Binomial cumulative sums of the (signless) central Stirling numbers of the first kind (A187646).

1, 2, 14, 262, 7740, 305536, 15061692, 890220752, 61347750704, 4829414749504, 427559293150976, 42047904926171552, 4547772798257998256, 536504774914535869664, 68557641564333466819744, 9433619169586732241895776

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*s(2k,k).

a(n) ~ exp((2*c-1)/(8*c^2)) * abs(Stirling1(2*n,n)) ~ 2^(3*n-1) * n^n * exp((2*c-1)/(8*c^2)-n) * c^(2*n) / (sqrt(Pi*n*(c-1)) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... - Vaclav Kotesovec, May 21 2014

Maple

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

Mathematica

Table[Sum[Binomial[n, k]Abs[StirlingS1[2k, k]], {k, 0, n}], {n, 0, 15}]

Prog

(Maxima) makelist(sum(binomial(n, k)*abs(stirling1(2*k, k)), k, 0, n), n, 0, 12);
(PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(2*k, k, 1))); \\ Michel Marcus, Aug 03 2021

Crossrefs

Cf. A187646.

Sequence in context: A070813 A156214 A370490 * A280517 A373222 A354511

Adjacent sequences: A187651 A187652 A187653 * A187655 A187656 A187657

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved