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A307444
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x*A(x))^(k+1).
3
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 08 2019
STATUS
approved