OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
FORMULA
G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} k!*binomial(j,k)*A(x)^k.
a(n) ~ exp(3) * n!. - Vaclav Kotesovec, Apr 10 2019
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 35*x^3 + 216*x^4 + 1527*x^5 + 11927*x^6 + 101056*x^7 + 920055*x^8 + 8960343*x^9 + 93202418*x^10 + ...
MATHEMATICA
terms = 22; A[_] = 1; Do[A[x_] = Sum[k! x^k A[x]^k/(1 - x)^(k + 1), {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
terms = 22; A[_] = 1; Do[A[x_] = Sum[x^j Sum[k! Binomial[j, k] A[x]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 08 2019
STATUS
approved