A385442 -id:A385442 - 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

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

Original entry on oeis.org

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

cp's OEIS Frontend

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

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