A377426 -id:A377426 - cp's OEIS frontend

A377427 E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^2))^2.

1, 2, 24, 574, 20950, 1034588, 64592556, 4881978904, 433485612000, 44236604978112, 5102049359506176, 656355318561027072, 93184708368255490896, 14472905373087118415040, 2441090221004851173202080, 444344375119629711627403776, 86822659466273927313499224192

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Cf. A377426, A377429.

Cf. A376392.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377426.

a(n) = (2/(4*n+2)!) * Sum_{k=0..n} (4*n+k+1)! * |Stirling1(n,k)|.

A377429 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^4 ).

Original entry on oeis.org

1, 4, 56, 1436, 54540, 2763696, 175688744, 13457185080, 1207241712536, 124205544781728, 14420516981211360, 1865347268407271040, 266056506383725529568, 41485848013549310521536, 7021170794004780911946048, 1281852242007649764308226240, 251124461130948243588667169280

Offset: 0

Seiichi Manyama, Oct 28 2024

nonn

Index entries for reversions of series

Cf. A052802, A376392, A376393.

Cf. A377426, A377427.

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^4)/x))

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

E.g.f. A(x) satisfies A(x) = 1/(1 + log(1 - x*A(x)))^4.
E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377426.
a(n) = (4/(4*n+4)!) * Sum_{k=0..n} (4*n+k+3)! * |Stirling1(n,k)|.

cp's OEIS Frontend

A377427 E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^2))^2.

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A377429 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^4 ).

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