A375717 -id:A375717 - cp's OEIS frontend

A375718 Expansion of e.g.f. 1 / sqrt(1 - x^3 * (exp(x) - 1)).

1, 0, 0, 0, 12, 30, 60, 105, 15288, 136332, 794160, 3742695, 165156420, 2977295178, 34259966832, 307175369865, 8066201665200, 210501545175960, 3893163654156768, 56023707973290507, 1275541469736173820, 38629328708426716470, 991445561747177496960

Offset: 0

Seiichi Manyama, Aug 25 2024

nonn

Cf. A358014, A375716, A375717.

Cf. A375701.

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

a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+3)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+3)) * Stirling2(n-3*k,k)/(6^k*(n-3k)!).

A375716 Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/6).

Original entry on oeis.org

1, 0, 0, 0, 4, 10, 20, 35, 3976, 35364, 205920, 970365, 37643980, 670990606, 7705037704, 69043474955, 1690055888080, 43135620048200, 793592298255936, 11401734214307769, 250361353418216340, 7380072768323315410, 187670442928777057480, 3868359812089009616071

Offset: 0

Seiichi Manyama, Aug 25 2024

nonn

Cf. A358014, A375717, A375718.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*(exp(x)-1))^(1/6)))

a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));

a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+1)) * Stirling2(n-3*k,k)/(6^k*(n-3k)!).

cp's OEIS Frontend

A375718 Expansion of e.g.f. 1 / sqrt(1 - x^3 * (exp(x) - 1)).

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A375716 Expansion of e.g.f. 1 / (1 - x^3 * (exp(x) - 1))^(1/6).

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