A385420 -id:A385420 - cp's OEIS frontend

A385422 Expansion of e.g.f. 1/(1 - arcsin(3*x))^(1/3).

1, 1, 4, 37, 424, 6889, 129376, 3004597, 78196864, 2363157937, 78520720384, 2924352594373, 118146438461440, 5232528466643737, 248845526415892480, 12778931460471237397, 699044652076991610880, 40846771050451091426785, 2526020027235443981025280

Offset: 0

Seiichi Manyama, Jun 28 2025

nonn

Cf. A189780, A385421.

Cf. A007559, A007788, A235135, A385343, A385420.

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-asin(3*x))^(1/3)))

a(n) = Sum_{k=0..n} A007559(k) * 3^(n-k) * A385343(n,k).

a(n) ~ sqrt(2*Pi) * cos(1)^(1/3) * 3^n * n^(n - 1/6) / (Gamma(1/3) * sin(1)^(n + 1/3) * exp(n)). - Vaclav Kotesovec, Jun 28 2025

A385419 Expansion of e.g.f. 1/(1 - arcsinh(2*x))^(1/2).

Original entry on oeis.org

1, 1, 3, 11, 57, 489, 5067, 50595, 573297, 9323985, 168823443, 2679252795, 45149256105, 1121782132665, 29930127386715, 629179051311315, 13329925622622945, 472248682257228705, 17395967794618282275, 434384524558247177835, 10095605146704332967705

Offset: 0

Seiichi Manyama, Jun 28 2025

sign

a(32) = -243211075187578815197768727974208613120575.

Cf. A296675, A385420.

Cf. A001147, A385371, A385343.

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-asinh(2*x))^(1/2)))

E.g.f.: 1/(1 - log(2*x + sqrt(4*x^2 + 1)))^(1/2).

a(n) = Sum_{k=0..n} A001147(k) * (2*i)^(n-k) * A385343(n,k), where i is the imaginary unit.

cp's OEIS Frontend

A385422 Expansion of e.g.f. 1/(1 - arcsin(3*x))^(1/3).

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