A377495 -id:A377495 - cp's OEIS frontend

A377490 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x*A(x)) - 1))^2.

1, 2, 24, 560, 19844, 949632, 57398980, 4197775472, 360541351092, 35581415127200, 3968076446262116, 493536896206210320, 67738259336620421140, 10170114513821104697792, 1658107523049271429191492, 291735781263854493014688944, 55097256018925972909190946932

Offset: 0

Seiichi Manyama, Oct 29 2024

nonn

Cf. A367162, A377491.

Cf. A377495.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377495.

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

A377498 E.g.f. satisfies A(x) = 1/(1 - A(x)^3 * (exp(x*A(x)^3) - 1)).

Original entry on oeis.org

1, 1, 15, 472, 23109, 1544236, 131066427, 13504084084, 1637471184585, 228472604080636, 36059751069011079, 6352095608437311844, 1235464848177560948685, 262972526121658780180300, 60804392657638382942192691, 15176441397584819546121452692, 4066926719970372629975938096017

Offset: 0

Seiichi Manyama, Oct 30 2024

nonn

Cf. A000670, A367162, A377495.

a(n) = sum(k=0, n, (3*n+4*k)!/(3*n+3*k+1)!*stirling(n, k, 2));

a(n) = Sum_{k=0..n} (3*n+4*k)!/(3*n+3*k+1)! * Stirling2(n,k).

cp's OEIS Frontend

A377490 E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x*A(x)) - 1))^2.

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