A380407 -id:A380407 - cp's OEIS frontend

A380426 E.g.f. A(x) satisfies A(x) = exp( 3 * x * A(x)^(1/3) * exp(x * A(x)^(1/3)) ).

1, 3, 21, 225, 3309, 62223, 1430235, 38940681, 1227116409, 43970226651, 1766653847079, 78696970239165, 3850658628709941, 205350233796536871, 11856632842453069491, 736988120901130761297, 49073265311942508067185, 3485242354486865203370931, 263004127262410708414755135

Offset: 0

Seiichi Manyama, Jan 24 2025

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..360

Cf. A162695, A380425, A380427.

Cf. A380407.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A162695.

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

A380406 E.g.f. satisfies A(x) = exp( 2 * x * exp(x) * A(x)^(1/2) ).

Original entry on oeis.org

1, 2, 12, 104, 1232, 18592, 342208, 7451264, 187631872, 5369721344, 172255038464, 6125052946432, 239195824279552, 10179739052908544, 469024768235192320, 23263095316577681408, 1235978286454556131328, 70040404736026578386944, 4217180561907991530176512

Offset: 0

Seiichi Manyama, Jan 23 2025

nonn

Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A273954, A357247, A380407.

Cf. A273953, A360473.

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A273954.
E.g.f.: A(x) = exp( -2*LambertW(-x * exp(x)) ).
a(n) = 2 * Sum_{k=0..n} k^(n-k) * (k+2)^(k-1) * binomial(n,k).
a(n) ~ 2 * sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (exp(n-2) * LambertW(exp(-1))^n). - Vaclav Kotesovec, Aug 05 2025

cp's OEIS Frontend

A380426 E.g.f. A(x) satisfies A(x) = exp( 3 * x * A(x)^(1/3) * exp(x * A(x)^(1/3)) ).

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