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A187661 Binomial convolution of the (signless) central Stirling numbers of the first kind and the central Stirling numbers of the second kind. 2
1, 2, 20, 369, 10192, 379850, 17930697, 1027046517, 69216504576, 5363945384274, 469658243947850, 45827641349686636, 4928867833029014503, 579101340954599901152, 73778702335232336908585, 10129059530832922239925140 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

FORMULA

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

a(n) ~ m * n^n * c^(2*n) * 2^(3*n-1) / (sqrt(Pi*(c-1)*n) * exp(n) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2) = 1.75643120862616967698..., and m = Sum_{j>=0} StirlingS2(2*j,j) * (2*c-1)^j / (j! * 2^(3*j) * c^(2*j)) = 1.170003674502655133465266152119563086693466... . - Vaclav Kotesovec, May 22 2014

MAPLE

seq(sum(binomial(n, k) * abs(combinat[stirling1](2*k, k)) * combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);

MATHEMATICA

Table[Sum[Binomial[n, k]Abs[StirlingS1[2k, k]]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 15}]

PROG

(Maxima) makelist(sum(binomial(n, k)*abs(stirling1(2*k, k))*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);

(PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(2*k, k, 1)*stirling(2*(n-k), n-k, 2))); \\ Michel Marcus, May 28 2017

CROSSREFS

Cf. A007820, A187646.

Sequence in context: A060164 A267827 A084948 * A263207 A218306 A009236

Adjacent sequences:  A187658 A187659 A187660 * A187662 A187663 A187664

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Mar 12 2011

STATUS

approved

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Last modified May 25 00:03 EDT 2022. Contains 354047 sequences. (Running on oeis4.)