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A258969 E.g.f.: A'(x) = 1 + A(x)^3, with A(0)=1. 7
1, 2, 6, 42, 390, 4698, 69174, 1203498, 24163110, 549811962, 13982486166, 393026414922, 12099527531910, 404881353252378, 14632253175107574, 567974815524008298, 23567351945550373350, 1040985881615266375482, 48767788927611416600406, 2415210691383917131432842 (list; graph; refs; listen; history; text; internal format)
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: A074021 A050862 A227250 * A161632 A115974 A179330

Adjacent sequences:  A258966 A258967 A258968 * A258970 A258971 A258972

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 15 2015

STATUS

approved

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Last modified February 25 11:17 EST 2018. Contains 299653 sequences. (Running on oeis4.)