A375809 -id:A375809 - cp's OEIS frontend

A375813 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^3.

1, 3, 12, 60, 396, 3240, 30960, 335160, 4072320, 54976320, 815119200, 13152585600, 229441766400, 4303027048320, 86318858545920, 1843929831744000, 41786821607731200, 1001231951502182400, 25288602517469491200, 671488122628741017600

Offset: 0

Seiichi Manyama, Aug 29 2024

nonn

Cf. A375796, A375812.

Cf. A375809.

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

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375796.

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

A375808 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^2.

Original entry on oeis.org

1, 2, 6, 24, 144, 1080, 9360, 94080, 1078560, 13789440, 194745600, 3013718400, 50654419200, 918900702720, 17896250211840, 372338481715200, 8241399758592000, 193366506222489600, 4793430516921446400, 125181207625240166400, 3435031723216084992000

Offset: 0

Seiichi Manyama, Aug 29 2024

nonn

Cf. A375799, A375809.

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

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375799.

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.

cp's OEIS Frontend

A375813 Expansion of e.g.f. 1/(1 - (exp(x^3) - 1)/x^2)^3.

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A375808 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^2.

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