A375688 -id:A375688 - cp's OEIS frontend

A375689 Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(2/3).

1, 0, 4, 6, 136, 660, 13188, 123480, 2584160, 37044000, 855658800, 16536548160, 428924382720, 10358056051200, 302474317729920, 8701780305254400, 284949736641177600, 9464366170599782400, 345224605512559518720, 12956112412535827353600

Offset: 0

Seiichi Manyama, Aug 24 2024

nonn

Cf. A367879, A375688.

Cf. A365575.

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

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

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

A375696 Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(1/3).

Original entry on oeis.org

1, 0, 2, 3, 52, 245, 4206, 37807, 712552, 9755433, 207915490, 3830073731, 92948571420, 2139142283005, 58945940093782, 1617324856023255, 50252559901690576, 1593701025177559121, 55366628370374688714, 1986560560083994301611

Offset: 0

Seiichi Manyama, Aug 24 2024

nonn

Cf. A367881, A375697.

Cf. A375688.

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

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

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

cp's OEIS Frontend

A375689 Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(2/3).

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A375696 Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(1/3).

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Author

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Crossrefs

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PARI

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Formula