A365778 - OEIS

A365778

Expansion of e.g.f. (exp(3*x) / (2 - exp(3*x)))^(1/6).

1, 1, 4, 37, 505, 9076, 202519, 5397337, 167237410, 5906437651, 234185226409, 10299442379062, 497567448860365, 26191947311138701, 1492143868674196924, 91466801447468838337, 6002791454773440431245, 419938013721629866235476

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = Sum_{k=0..n} (-3)^(n-k) * (Product_{j=0..k-1} (6*j+1)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-3)^k * (5/3 * k/n - 2) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = a(n-1) + Sum_{k=1..n-1} 3^k * binomial(n-1,k) * a(n-k).

PROG

(PARI) a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, 6*j+1)*stirling(n, k, 2));

CROSSREFS

Cf. A365779.

Sequence in context: A235135 A316877 A349254 * A277638 A352237 A349714

Adjacent sequences: A365775 A365776 A365777 * A365779 A365780 A365781

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 16 2023

STATUS

approved