A375878 E.g.f. satisfies A(x) = 1/(1 - x)^(2*A(x)^(1/2)).

1, 2, 10, 78, 832, 11320, 187968, 3693760, 83970640, 2170052928, 62876256000, 2019782393904, 71268840658464, 2740911076718256, 114134851494134352, 5116804468061982000, 245747690114319479808, 12589481527535031074304, 685316177026591879217664

Offset: 0

Author

Seiichi Manyama, Sep 01 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A052813, A375879.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*lambertw(log(1-x)))))

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052813.

E.g.f.: exp( - 2*LambertW(log(1 - x)) ).

a(n) = 2 * Sum_{k=0..n} (k+2)^(k-1) * |Stirling1(n,k)|.

a(n) ~ 2 * n^(n-1) / ((exp(exp(-1)) - 1)^(n - 1/2) * exp(n - n*exp(-1) - 5/2)). - Vaclav Kotesovec, Aug 05 2025