A351734 - OEIS

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A351734

Expansion of e.g.f. exp( 3 * x * (exp(x) - 1) ).

1, 0, 6, 9, 120, 555, 5148, 39711, 378528, 3715011, 39838260, 452684463, 5463506304, 69553644771, 930940368036, 13054086036855, 191222363275968, 2918620069099395, 46309955947643124, 762335523354333855, 12995722456718984160, 229045407317491457763

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = n! * Sum_{k=0..floor(n/2)} 3^k * Stirling2(n-k,k)/(n-k)!.

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(3*x*(exp(x)-1))))

(PARI) a(n) = n!*sum(k=0, n\2, 3^k*stirling(n-k, k, 2)/(n-k)!);

CROSSREFS

Cf. A052506, A351733.

Cf. A053490, A351737.

Sequence in context: A121233 A156180 A191011 * A053490 A265383 A375661

Adjacent sequences: A351731 A351732 A351733 * A351735 A351736 A351737

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 20 2022

STATUS

approved