A377498 -id:A377498 - cp's OEIS frontend

A377495 E.g.f. satisfies A(x) = 1/(1 - A(x)^2 * (exp(x*A(x)^2) - 1)).

1, 1, 11, 247, 8571, 404791, 24246439, 1761559647, 150540054611, 14798051914231, 1645040516034927, 204068062926942655, 27946847973073178587, 4188043229601371413911, 681707014005609312133175, 119774859918869807700934111, 22592863584958717501615734051, 4553853548371236985017395321335

Offset: 0

Seiichi Manyama, Oct 29 2024

nonn

Cf. A000670, A367162, A377498.

Cf. A377490.

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

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

A377491 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x*A(x)) - 1))^3.

Original entry on oeis.org

1, 3, 51, 1692, 85245, 5799348, 498288327, 51799641372, 6323803975545, 887056541576820, 140606281908386763, 24856199282033820396, 4848804928048309664181, 1034685331580238018659748, 239758404709207383049312239, 59955226332194712661373725884

Offset: 0

Seiichi Manyama, Oct 29 2024

nonn

Cf. A367162, A377490.

Cf. A377498.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377498.

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

cp's OEIS Frontend

A377495 E.g.f. satisfies A(x) = 1/(1 - A(x)^2 * (exp(x*A(x)^2) - 1)).

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