A377545 -id:A377545 - 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)! ).

A377541 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^2.

Original entry on oeis.org

1, 2, 10, 90, 1184, 20650, 450252, 11803526, 361892848, 12712357170, 503564718260, 22212233618542, 1079909444635848, 57379354040049002, 3308238701451609772, 205715613407117613270, 13724187813695296374752, 977841609869801208944482, 74108335568947966714172004

Offset: 0

Seiichi Manyama, Oct 31 2024

nonn

Cf. A161633, A377545, A377551.

Cf. A364980.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364980.

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