A377424 - OEIS

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

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

a(n) ~ 2^(6*n-1) * LambertW(exp(1/4)/2)^(4*n+1) * n^(n-1) / (sqrt(1 + LambertW(exp(1/4)/2)) * exp(n) * (4*LambertW(exp(1/4)/2) - 1)^(5*n+1)). - Vaclav Kotesovec, Feb 02 2026

MATHEMATICA

Table[1/(4*n+1)! * Sum[(4*n+k)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 02 2026 *)

PROG

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

CROSSREFS

Cf. A000670, A052894, A367134, A367135.

Cf. A377425, A377428.

Sequence in context: A274129 A346896 A012154 * A009055 A009067 A128683

Adjacent sequences: A377421 A377422 A377423 * A377425 A377426 A377427

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 28 2024

STATUS

approved