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URL: https://oeis.org/A307442

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A307442
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 - x*A(x))^(k+1).
3
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 08 2019
STATUS
approved