A377550 -id:A377550 - cp's OEIS frontend

A377551 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^4.

1, 4, 28, 348, 6424, 156900, 4788024, 175678468, 7538078944, 370557062532, 20540717542120, 1267858489975044, 86252943572785488, 6412719306748404676, 517341051818833834648, 45012757582472804739780, 4201834386001491870902464, 418891045572216881436564228

Offset: 0

Seiichi Manyama, Oct 31 2024

nonn

Cf. A161633, A377541, A377545.

Cf. A377550, A377552.

a(n) = 4*n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+4, k)/((4*n-3*k+4)*(n-k)!));

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377550.

a(n) = 4 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+4,k)/( (4*n-3*k+4)*(n-k)! ).

A377552 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)^2))^2.

Original entry on oeis.org

1, 2, 10, 114, 2000, 47050, 1399452, 50386406, 2130643216, 103530094866, 5684985037460, 348165567064942, 23530146364469208, 1739586913373486138, 139658209205202262876, 12099843726478251739830, 1125274333255817053205792, 111809642081518362872011042, 11821367007844973309548419876

Offset: 0

Seiichi Manyama, Oct 31 2024

nonn

Cf. A377550, A377551.

a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+2, k)/((4*n-3*k+2)*(n-k)!));

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377550.

a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+2,k)/( (4*n-3*k+2)*(n-k)! ).

cp's OEIS Frontend

A377551 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^4.

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