A371142 -id:A371142 - cp's OEIS frontend

A371143 E.g.f. satisfies A(x) = 1 + xA(x)^3 (exp(x) - 1).

1, 0, 2, 3, 76, 365, 9906, 94507, 2832824, 43209945, 1438766830, 30971280791, 1146868043124, 32166137748901, 1322928667341386, 45791799761422275, 2085517396191903856, 85748423669245738673, 4306944218393176448742, 204597526239295278145327

Offset: 0

Seiichi Manyama, Mar 12 2024

nonn

Cf. A052848, A371142.

Cf. A371141.

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

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

A377719 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^2.

Original entry on oeis.org

1, 0, 4, 6, 128, 610, 12192, 112154, 2416416, 34337538, 827541200, 16047333082, 436958019984, 10718568174626, 329594991463584, 9737689680629850, 336439401299953472, 11581626068262440194, 446492838289046854320, 17496904148975860376474, 747070411957344952492080

Offset: 0

Seiichi Manyama, Nov 04 2024

nonn

Cf. A371142, A377438.

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

E.g.f.: 4/(1 + sqrt(1 - 4*x*(exp(x) - 1)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371142.
a(n) = 2 * n! * Sum_{k=0..floor(n/2)} (2*k+1)! * Stirling2(n-k,k)/( (n-k)! * (k+2)! ).

cp's OEIS Frontend

A371143 E.g.f. satisfies A(x) = 1 + xA(x)^3 (exp(x) - 1).

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A377719 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^2.

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PARI

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cp's OEIS Frontend

A371143 E.g.f. satisfies A(x) = 1 + x*A(x)^3 * (exp(x) - 1).

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Author

Keywords

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Programs

PARI

Formula

A377719 E.g.f. satisfies A(x) = (1 + x * (exp(x) - 1) * A(x))^2.

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A371143 E.g.f. satisfies A(x) = 1 + xA(x)^3 (exp(x) - 1).