A307444 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x*A(x))^(k+1).

1, 0, 1, 2, 11, 54, 336, 2330, 18359, 161660, 1580853, 17031728, 200718372, 2569989304, 35531288796, 527506796282, 8368806193151, 141271243571640, 2527897717923387, 47789579768358498, 951677263953890739, 19910429474370487166, 436589745454529328720, 10012315468481417357976

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000166(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x/Sum_{k>=0} A000166(k)*x^k).

a(n) ~ exp(-1) * n!. - Vaclav Kotesovec, Apr 10 2019

Example

G.f.: A(x) =  1 + x^2 + 2*x^3 + 11*x^4 + 54*x^5 + 336*x^6 + 2330*x^7 + 18359*x^8 + 161660*x^9 + 1580853*x^10 + ...

Mathematica

terms = 24; CoefficientList[1/x InverseSeries[Series[x/Sum[Subfactorial[k] x^k, {k, 0, terms}], {x, 0, terms}], x], x]
terms = 24; A[_] = 1; Do[A[x_] = Sum[k! x^k A[x]^k/(1 + x A[x])^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 24; A[_] = 1; Do[A[x_] = Sum[Subfactorial[k] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A000166, A088368, A307441, A307442, A307443.

Sequence in context: A128748 A251662 A327215 * A037522 A037731 A221019

Adjacent sequences: A307441 A307442 A307443 * A307445 A307446 A307447

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 08 2019

Status

approved