A318365 -id:A318365 - cp's OEIS frontend

A321989 Expansion of e.g.f. exp(exp(-x)/(1 - x) - 1).

1, 0, 1, 2, 12, 64, 455, 3618, 33131, 338728, 3838572, 47678520, 644172045, 9402091620, 147405489205, 2470129035710, 44053120590540, 833000495161600, 16644648834503555, 350406040769989974, 7751328201878523295, 179738821179613739780, 4359334293132050359932, 110368937036048741434824

Offset: 0

Ilya Gutkovskiy, Dec 19 2018

nonn

Cf. A000166, A000262, A318365, A321974.

seq(coeff(series(factorial(n)*exp(exp(-x)/(1-x)-1),x,n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Dec 19 2018

nmax = 23; CoefficientList[Series[Exp[Exp[-x]/(1 - x) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Subfactorial[k] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

a(0) = 1; a(n) = Sum_{k=1..n} A000166(k)*binomial(n-1,k-1)*a(n-k).

a(n) ~ exp(3*exp(-1)/2 - 5/4 + 2*exp(-1/2)*sqrt(n) - n) * n^(n-1/4) / sqrt(2). - Vaclav Kotesovec, Dec 19 2018

A318364 Expansion of e.g.f. exp(x*exp(x)/(1 - x)).

Original entry on oeis.org

1, 1, 5, 28, 197, 1676, 16597, 186796, 2350105, 32634928, 495207881, 8144456684, 144204493765, 2733218222944, 55188182951917, 1182163846918156, 26765995313355953, 638508459302742464, 16002492517241163793, 420279349847440766284, 11540406000681962458141, 330624627443307824367616

Offset: 0

Ilya Gutkovskiy, Aug 24 2018

nonn

Cf. A000248, A000262, A000522, A007526, A318365.

a:=series(exp(x*exp(x)/(1 - x)), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019

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

x = 'x + O('x^25); Vec(serlaplace(exp(x*exp(x)/(1 - x)))) \\ Michel Marcus, Aug 25 2018

a(0) = 1; a(n) = Sum_{k=1..n} A007526(k)*binomial(n-1,k-1)*a(n-k).

a(n) ~ exp(1/4 - 3*exp(1)/2 + 2*exp(1/2)*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Aug 25 2018

cp's OEIS Frontend

A321989 Expansion of e.g.f. exp(exp(-x)/(1 - x) - 1).

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