A332254 E.g.f.: 1 / (2 - exp(exp(x) - 1 - x)).

1, 0, 1, 1, 10, 31, 271, 1534, 14603, 120173, 1310224, 13947517, 175477699, 2265702388, 32673218085, 492565328493, 8053045395018, 138334722101571, 2535114408394699, 48790865853110950, 991843960201311455, 21121971129683138297, 471959969940724275432

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A000296(k) * a(n-k).

a(n) ~ n! * exp(1 - exp(c-1)/2) / ((1 - 2*exp(1-c)) * (c - 1 - log(2))^(n+1)), where c = -LambertW(-1, -exp(-1)/2) = 2.678346990016660653412884512094523... - Vaclav Kotesovec, Feb 08 2020

Mathematica

nmax = 22; CoefficientList[Series[1/(2 - Exp[Exp[x] - 1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) seq(n)={Vec(serlaplace(1/(2 - exp(exp(x + O(x*x^n)) - 1 - x))))} \\ Andrew Howroyd, Feb 08 2020

Crossrefs

Cf. A000296, A028248, A083355, A293037.

Sequence in context: A289201 A042849 A097236 * A280202 A061485 A136335

Adjacent sequences: A332251 A332252 A332253 * A332255 A332256 A332257

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 08 2020

Status

approved