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URL: https://oeis.org/A307443

⇱ A307443 - OEIS

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A307443
G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 + x)^(k+1).
3
1, 0, 1, 3, 14, 73, 439, 2986, 22849, 195639, 1864072, 19639587, 227216485, 2866190328, 39155468153, 575750407431, 9063067630294, 152007287492665, 2705337486885751, 50909087031293746, 1009776468826520181, 21052688394533433215, 460223336063328374304, 10525518902412521320567
OFFSET
0,4
FORMULA
G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} (-1)^(j-k)*k!*binomial(j,k)*A(x)^k.
a(n) ~ exp(-1) * n!. - Vaclav Kotesovec, Apr 10 2019
EXAMPLE
G.f.: A(x) = 1 + x^2 + 3*x^3 + 14*x^4 + 73*x^5 + 439*x^6 + 2986*x^7 + 22849*x^8 + 195639*x^9 + 1864072*x^10 + ...
MATHEMATICA
terms = 24; 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 = 24; A[_] = 1; Do[A[x_] = Sum[x^j Sum[(-1)^(j - k) 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