A321974 Expansion of e.g.f. exp(exp(x)/(1 - x) - 1).

1, 2, 9, 54, 404, 3598, 37003, 430300, 5571147, 79358032, 1231990840, 20684884234, 373208232229, 7197079035318, 147658793214733, 3210107125516682, 73690798853163884, 1780718798351625094, 45171972342078432287, 1199948465249850848608, 33305064129201851432591, 963911863209583899492324

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A000522(k)*binomial(n-1,k-1)*a(n-k).

a(n) ~ exp(-exp(1)/2 - 3/4 + 2*exp(1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Dec 19 2018

Maple

seq(n!*coeff(series(exp(exp(x)/(1 - x) - 1), x=0, 22), x, n), n=0..21); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 21; CoefficientList[Series[Exp[Exp[x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Floor[Exp[1] k!] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000262, A000522, A318364, A321989.

Sequence in context: A000168 A307442 A222014 * A127128 A353255 A254795

Adjacent sequences: A321971 A321972 A321973 * A321975 A321976 A321977

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 19 2018

Status

approved