A307442 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 - x*A(x))^(k+1).

1, 2, 9, 54, 379, 2948, 24736, 220622, 2074775, 20491386, 212312349, 2310232488, 26473612772, 320735694048, 4126350096188, 56601987176510, 830233489763775, 13036492313617494, 218958840306428947, 3924128327446669670, 74779561501535316579, 1509296316416028136188

Offset

0,2

Links

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

Formula

G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000522(k)*x^k*A(x)^k.

G.f.: A(x) = (1/x)*Series_Reversion(x/Sum_{k>=0} A000522(k)*x^k).

a(n) ~ exp(3) * n!. - Vaclav Kotesovec, Apr 10 2019

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 54*x^3 + 379*x^4 + 2948*x^5 + 24736*x^6 + 220622*x^7 + 2074775*x^8 + 20491386*x^9 + 212312349*x^10 + ...

Mathematica

terms = 22; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[Floor[Exp[1] k!] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]
terms = 22; 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 = 22; A[_] = 1; Do[A[x_] = 1 + Sum[Floor[Exp[1] k!] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A000522, A088368, A307441, A307443, A307444.

Sequence in context: A089436 A368178 A000168 * A222014 A321974 A127128

Adjacent sequences: A307439 A307440 A307441 * A307443 A307444 A307445

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 08 2019

Status

approved