A307439 G.f. A(x) satisfies: A(x) = Sum_{j>=0} j!*x^j*A(x)^j / Product_{k=1..j} (1 - k*x).

1, 1, 4, 22, 150, 1198, 10900, 111392, 1268816, 16029676, 223672208, 3431679208, 57595357568, 1051552630592, 20766322925296, 441147381668704, 10029896993061488, 242949296094059648, 6244343162806585552, 169693360047016652048, 4860575220802324411120, 146335002352369970686352

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

G.f. A(x) satisfies: A(x) = Sum_{j>=0} x^j * Sum_{k=0..j} k!*Stirling2(j,k)*A(x)^k.

a(n) ~ exp(1/2) * n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Apr 10 2019

Example

G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 150*x^4 + 1198*x^5 + 10900*x^6 + 111392*x^7 + 1268816*x^8 + 16029676*x^9 + 223672208*x^10 + ...

Mathematica

terms = 22; A[_] = 1; Do[A[x_] = Sum[j! x^j A[x]^j/Product[(1 - k 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]^k, {k, 0, j}], {j, 0, i}] + O[x]^i, {i, 1, terms}]; CoefficientList[A[x], x]

Crossrefs

Cf. A000670, A019538, A225293, A225294, A307402, A307440.

Sequence in context: A111529 A346764 A228883 * A189845 A039304 A349022

Adjacent sequences: A307436 A307437 A307438 * A307440 A307441 A307442

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 08 2019

Status

approved