A318364 -id:A318364 - cp's OEIS frontend

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

Ilya Gutkovskiy, Dec 19 2018

nonn

Cf. A000262, A000522, A318364, A321989.

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

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}]

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

A318365 Expansion of e.g.f. exp(x*exp(-x)/(1 - x)).

Original entry on oeis.org

1, 1, 1, 4, 21, 116, 805, 6504, 59353, 608320, 6901641, 85824080, 1160786341, 16959401304, 266133942061, 4463567862376, 79669223849265, 1507610621184224, 30145968665822737, 635066714078714016, 14057275047440540221, 326159212986987669640, 7915118313077599105461, 200503241124736099689656

Offset: 0

Ilya Gutkovskiy, Aug 24 2018

nonn

Cf. A000166, A000240, A000262, A003725, A318364.

seq(n!*coeff(series(exp(x*exp(-x)/(1-x)),x=0,24),x,n),n=0..23); # Paolo P. Lava, Jan 09 2019

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

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} A000240(k)*binomial(n-1,k-1)*a(n-k).

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

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Formula