VOOZH about

URL: https://oeis.org/A307440

⇱ A307440 - OEIS

login
A307440
G.f. A(x) satisfies: A(x) = Sum_{j>=0} j!*x^j / Product_{k=1..j} (1 - k*x*A(x)).
2
1, 1, 3, 14, 86, 647, 5739, 58647, 679513, 8818219, 126887789, 2007051456, 34634864692, 647737588429, 13052029344893, 281915983915202, 6497718168838214, 159172833649907801, 4129605445474716345, 113112957674428539930, 3261790879443599064394, 98772906841120521388973
OFFSET
0,3
LINKS
FORMULA
G.f. satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} k!*Stirling2(j,k)*A(x)^(j-k).
a(n) ~ exp(-1/2) * n! / (log(2))^(n+1). - Vaclav Kotesovec, Apr 10 2019
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 14*x^3 + 86*x^4 + 647*x^5 + 5739*x^6 + 58647*x^7 + 679513*x^8 + 8818219*x^9 + 126887789*x^10 + ...
MATHEMATICA
terms = 22; A[_] = 1; Do[A[x_] = Sum[j! x^j/Product[(1 - k x A[x]), {k, 1, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]
terms = 22; A[_] = 1; Do[A[x_] = Sum[x^j Sum[k! StirlingS2[j, k] A[x]^(j - 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