A377541 -id:A377541 - 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)! ).

A377545 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^3.

Original entry on oeis.org

1, 3, 18, 195, 3108, 65595, 1730538, 54891165, 2036187576, 86536398195, 4147191867630, 221314773837333, 13017260705093604, 836754118106509083, 58364080427471191506, 4390560359156841730605, 354356981533262814367728, 30543768949098926368973667, 2800395449868306713606542422

Offset: 0

Seiichi Manyama, Oct 31 2024

nonn

Cf. A161633, A377541, A377551.

Cf. A364981.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364981.

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