A307441 G.f. A(x) satisfies: A(x) = Sum_{k>=0} k!*x^k*A(x)^k/(1 - x)^(k+1).

1, 2, 7, 35, 216, 1527, 11927, 101056, 920055, 8960343, 93202418, 1035640333, 12305625141, 156513872514, 2131781868823, 31077520424879, 484157377851360, 8040920113043655, 141937291242762263, 2654252437895865112, 52412046969340405371, 1089506079309378596823

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

Cf. A000522, A088368, A307442, A307443, A307444.

Sequence in context: A003575 A043546 A350309 * A260530 A201690 A080831

Adjacent sequences: A307438 A307439 A307440 * A307442 A307443 A307444

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 08 2019

Status

approved