A377428 -id:A377428 - cp's OEIS frontend

A377424 E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^4)).

1, 1, 11, 253, 9019, 438021, 26992707, 2018069341, 177498369419, 17959376607061, 2055112480694323, 262437681414074541, 36999068388057870651, 5708040382071000644581, 956533539112835413864739, 173022072326584494697760893, 33600521994423195247370822251, 6972639514725247888782370422261

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Cf. A000670, A052894, A367134, A367135.

Cf. A377425, A377428.

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

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

A377425 E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^2))^2.

Original entry on oeis.org

1, 2, 24, 572, 20788, 1021892, 63498116, 4776128772, 422019084132, 42854861672612, 4918270207805188, 629575456637707076, 88938171122678982692, 13744507646644260776292, 2306659049841490720035780, 417774877069420589127228164, 81222489094387608969950071780

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Cf. A367134, A376389.

Cf. A377424, A377428.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377424.

a(n) = (2/(4*n+2)!) * Sum_{k=0..n} (4*n+k+1)! * Stirling2(n,k).

cp's OEIS Frontend

A377424 E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^4)).

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