A258969 E.g.f.: A'(x) = 1 + A(x)^3, with A(0)=1.

1, 2, 6, 42, 390, 4698, 69174, 1203498, 24163110, 549811962, 13982486166, 393026414922, 12099527531910, 404881353252378, 14632253175107574, 567974815524008298, 23567351945550373350, 1040985881615266375482, 48767788927611416600406, 2415210691383917131432842

Offset

0,2

Comments

Conjecture: A227250(n+1) = a(n).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ (3/(Pi/sqrt(3)-log(2)))^(n+1/2) * n^n / exp(n).

E.g.f.: 1 + Series_Reversion( Integral 1/((2+x)*(1+x+x^2)) dx ). - Paul D. Hanna, Jun 16 2015

Example

A(x) = 1 + 2*x + 6*x^2/2! + 42*x^3/3! + 390*x^4/4! + 4698*x^5/5! + ...
A'(x) = 2 + 6*x + 21*x^2 + 65*x^3 + 783*x^4/4 + 11529*x^5/20 + ...
1 + A(x)^3 = 2 + 6*x + 21*x^2 + 65*x^3 + 783*x^4/4 + 11529*x^5/20 + ...

Mathematica

nmax=20; Subscript[a, 0]=1; egf=Sum[Subscript[a, k]*x^k, {k, 0, nmax+1}]; Table[Subscript[a, k]*k!, {k, 0, nmax}] /.Solve[Take[CoefficientList[Expand[1+egf^3-D[egf, x]], x], nmax]==ConstantArray[0, nmax]][[1]]

Prog

 (PARI) {a(n) = local(A=1); A = 1 + serreverse( intformal( 1/((2+x)*(1+x+x^2) +x*O(x^n)) )); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Jun 16 2015

Crossrefs

Cf. A000831, A024396, A193534, A227250, A258970, A258971, A258880, A258994.

Sequence in context: A364407 A050862 A227250 * A161632 A115974 A179330

Adjacent sequences: A258966 A258967 A258968 * A258970 A258971 A258972

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2015

Status

approved