A377450 -id:A377450 - cp's OEIS frontend

A377451 E.g.f. satisfies A(x) = 1/(1 - A(x)^4 * (exp(x) - 1)).

1, 1, 11, 241, 8171, 377401, 22118531, 1572752161, 131565858491, 12661132904521, 1378019469008051, 167374385250354481, 22443998566390975211, 3293411316452536046041, 524941525063836265071971, 90316250360918785641307201, 16682672480771981403086626331, 3292860351837963891732540729961

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Cf. A367161, A377450.

Cf. A377454.

a(n) = sum(k=0, n, (5*k)!/(4*k+1)!*stirling(n, k, 2));

a(n) = Sum_{k=0..n} (5*k)!/(4*k+1)! * Stirling2(n,k).

A377453 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^3.

Original entry on oeis.org

1, 3, 33, 639, 18177, 687663, 32585793, 1858893039, 124128928257, 9502575055983, 820716875385153, 78959656742857839, 8375163183606235137, 971063889443489669103, 122194096152956362997313, 16586054767142612489229039, 2415658529914018225123490817, 375779208568915395913102663023

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Cf. A052895, A377452, A377454.

Cf. A377450.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377450.

a(n) = 3 * Sum_{k=0..n} (4*k+2)!/(3*k+3)! * Stirling2(n,k).

cp's OEIS Frontend

A377451 E.g.f. satisfies A(x) = 1/(1 - A(x)^4 * (exp(x) - 1)).

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