A375813 -id:A375813 - cp's OEIS frontend

A375809 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^3.

1, 3, 12, 60, 396, 3240, 30960, 337680, 4152960, 56790720, 853675200, 13990838400, 248242579200, 4739385530880, 96860893409280, 2109714647040000, 48780176949504000, 1193187564259891200, 30781385655513292800, 835194405961256140800

Offset: 0

Seiichi Manyama, Aug 29 2024

nonn

Cf. A375799, A375808.

Cf. A375813.

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)^3))

a(n) = n!*sum(k=0, n\3, (n-3*k+2)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!)/2;

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375799.

a(n) = (n!/2) * Sum_{k=0..floor(n/3)} (n-3*k+2)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.

A375812 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^2.

Original entry on oeis.org

1, 2, 6, 24, 144, 1080, 9360, 92400, 1038240, 13063680, 181137600, 2744280000, 45145900800, 801313793280, 15256927445760, 310158565516800, 6705376386508800, 153609543947059200, 3716764672074854400, 94715288771578675200, 2535525218048030208000

Offset: 0

Seiichi Manyama, Aug 29 2024

nonn

Cf. A375796, A375813.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^3)-1)/x^2)^2))

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375796.

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * Stirling2(n-2*k,n-3*k)/(n-2*k)!.

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A375809 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^3.

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A375812 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^2.

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