A377424 -id:A377424 - cp's OEIS frontend

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

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).

A377428 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^4 ).

Original entry on oeis.org

1, 4, 56, 1432, 54184, 2734104, 173032680, 13192623448, 1177932112040, 120610734752920, 13935516914366824, 1793837540679492312, 254604546529825454376, 39504947952102355425304, 6652925600854130108675048, 1208610940763303680263653464, 235601431979292206398224418216

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Index entries for reversions of series

Cf. A052894, A376389, A376390.

Cf. A377424, A377425.

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(2-exp(x))^4)/x))

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

E.g.f. A(x) satisfies A(x) = 1/(2 - exp(x*A(x)))^4.
E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377424.
a(n) = (4/(4*n+4)!) * Sum_{k=0..n} (4*n+k+3)! * Stirling2(n,k).

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A377428 Expansion of e.g.f. (1/x) * Series_Reversion( x*(2 - exp(x))^4 ).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula