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A256018 a(n) = Sum_{k=1..n} k^2*Bernoulli(k-1)*C(2*n-1,k)*Stirling2(2*n-k,n). 0
1, 3, 20, 245, 4494, 110187, 3383666, 124856160, 5380031514, 265119271131, 14704940493880, 906574369154181, 61497905451691500, 4552012167030253980, 365078953020578097000, 31536857167074430123800, 2919211651494480205278954, 288260464251527357838892875 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n) ~ sqrt(1-c) * 2^(2*n-1/2) * n^(n-3/2) / (sqrt(Pi) * exp(n) * (c*(2-c))^(n-1)), where c = -A226775 = -LambertW(-2*exp(-2)) = 0.4063757399599599... . - Vaclav Kotesovec, Jun 01 2015

a(n) = -Sum_{k=1..n} k^2*Bern(k-1)*C(2*n-1, k-1)*Stirling2(2*n-k, n), n>1, a(1)=1. - Vladimir Kruchinin, Jun 02 2015

MAPLE

seq(add(k^2*bernoulli(k-1)*binomial(2*n-1, k)*Stirling2(2*n-k, n), k=1..n), n=1..20); # Robert Israel, Jun 01 2015

MATHEMATICA

Table[Sum[k^2*BernoulliB[k-1]*Binomial[2*n-1, k]*StirlingS2[2*n-k, n], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jun 01 2015 *)

PROG

(Maxima)

makelist(sum(k^2*bern(k-1)*binomial(2*n-1, k)*stirling2(2*n-k, n), k, 1, n), n, 1, 30);

(PARI) a(n) = sum(k=1, n, k^2*bernfrac(k-1)*binomial(2*n-1, k)*stirling(2*n-k, n, 2)); \\ Michel Marcus, Jun 01 2015

(Maxima)

makelist(if n=1 then 1 else -sum(k^2*bern(k-1)*binomial(2*n-1, k-1)*stirling2(2*n-k, n), k, 1, n), n, 1, 30); /* Vladimir Kruchinin, Jun 02 2015 */

CROSSREFS

Cf. A027641, A027642.

Sequence in context: A200527 A237431 A237652 * A227469 A262208 A183607

Adjacent sequences:  A256015 A256016 A256017 * A256019 A256020 A256021

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Jun 01 2015

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)