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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..258 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 Cf. A000670, A019538, A225293, A225294, A307402, A307439. Sequence in context: A276313 A074520 A127715 * A087912 A308878 A051818 Adjacent sequences:  A307437 A307438 A307439 * A307441 A307442 A307443 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 08 2019 STATUS approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)