A363479 -id:A363479 - cp's OEIS frontend

A363358 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x)^2)).

1, 1, 7, 91, 1809, 48521, 1643863, 67381875, 3243606817, 179405231761, 11213025902631, 781604862035339, 60120379931640625, 5058593367221610009, 462199816484860893559, 45574025454771003821731, 4823543138131670132557377, 545448517762149418525390625

Offset: 0

Seiichi Manyama, Aug 17 2023

nonn

Cf. A362773, A363357.
Cf. A088695, A363479.
Cf. A361093.

a(n) = n!*sum(k=0, n, (2*n+1)^(k-1)*binomial(k, n-k)/k!);

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(k,n-k)/k!.

A365058 E.g.f. satisfies A(x) = exp(x * A(x)^3 * (1 + x/2 * A(x)^3)).

Original entry on oeis.org

1, 1, 8, 130, 3250, 110336, 4744984, 247321096, 15155937500, 1067967873280, 85084447796416, 7562971176299936, 742055168686622872, 79662784245760000000, 9288538211005096189280, 1168938868353871429273216, 157924822350438542185141264

Offset: 0

Seiichi Manyama, Aug 19 2023

nonn

Cf. A091485, A365057.

Cf. A363479.

a(n) = n!*sum(k=0, n, (1/2)^(n-k)*(3*n+1)^(k-1)*binomial(k, n-k)/k!);

a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (3*n+1)^(k-1) * binomial(k,n-k)/k!.

cp's OEIS Frontend

A363358 E.g.f. satisfies A(x) = exp(x * A(x)^2 * (1 + x * A(x)^2)).

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