A385440 -id:A385440 - cp's OEIS frontend

A385441 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^3) ).

1, 1, 7, 99, 2145, 62985, 2340135, 105306075, 5568833025, 338526428625, 23261601738375, 1783052341945875, 150846228128621025, 13961656447904590425, 1403387191229030382375, 152244874971071908900875, 17729607712540283209274625, 2206069759660369525039742625, 292095560880436494680262138375

Offset: 0

Seiichi Manyama, Jun 29 2025

nonn

Cf. A001147, A385369, A385440, A385442.

Cf. A385343.

a(n) = 2^n*n!*binomial((4*n+1)/2, n)/(4*n+1);

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

A385441 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^3) ).

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