A377425 -id:A377425 - 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).

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

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

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

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