A385441 -id:A385441 - cp's OEIS frontend

A385440 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^2) ).

1, 1, 5, 48, 693, 13440, 328185, 9676800, 334639305, 13284311040, 595505854125, 29756856729600, 1640160546688125, 98860780014796800, 6469121228247302625, 456736803668361216000, 34607895888408878660625, 2801319062499282124800000, 241247999301688986945463125

Offset: 0

Seiichi Manyama, Jun 29 2025

nonn

Cf. A001147, A385369, A385441, A385442.

Cf. A381415, A385343.

a(n) = 2^n*n!*binomial((3*n+1)/2, n)/(3*n+1);

E.g.f. A(x) satisfies A(x) = (1 + 2*x*A(x)^3)^(1/2).
a(n) = 2^n * n! * binomial((3*n+1)/2,n)/(3*n+1).
a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
a(n) ~ 3^(3*n/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jul 04 2025

A385442 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^4) ).

Original entry on oeis.org

1, 1, 9, 168, 4845, 190080, 9454725, 570286080, 40454959545, 3300640358400, 304513870485825, 31348317192192000, 3562533636856719525, 443003419150516224000, 59834227558379509360125, 8722929933255903805440000, 1365222778354029313094000625, 228317457245013328565108736000

Offset: 0

Seiichi Manyama, Jun 29 2025

nonn

Cf. A001147, A385369, A385440, A385441.

Cf. A385343.

a(n) = 2^n*n!*binomial((5*n+1)/2, n)/(5*n+1);

E.g.f. A(x) satisfies A(x) = (1 + 2*x*A(x)^5)^(1/2).
a(n) = 2^n * n! * binomial((5*n+1)/2,n)/(5*n+1).
a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
a(n) ~ 5^(5*n/2) * n^(n-1) / (exp(n) * 3^(3*n/2 + 1)). - Vaclav Kotesovec, Jul 04 2025

cp's OEIS Frontend

A385440 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^2) ).

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