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 A258970 E.g.f.: A'(x) = 1 + A(x)^4, with A(0)=1. 5
 1, 2, 8, 80, 1088, 19328, 422912, 10987520, 330555392, 11300913152, 432717037568, 18344259092480, 852932666851328, 43157160112160768, 2360748463307620352, 138821061188696145920, 8732741520836633034752, 585172975239737913638912, 41612642758392039581155328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..100 FORMULA a(n) ~ n! * d^(n+1/3) / (3^(1/3) * GAMMA(1/3) * n^(2/3)), where d = 1 / Sum_{j>=1} (-1)^(j+1)/(4*j-1) = 4*sqrt(2)/(Pi + log(3-2*sqrt(2))) = 4.10260201986929... E.g.f.: 1 + Series_Reversion( Integral 1/(1 + (1+x)^4) dx ). - Paul D. Hanna, Jun 16 2015 EXAMPLE A(x) = 1 + 2*x + 8*x^2/2! + 80*x^3/3! + 1088*x^4/4! + 19328*x^5/5! + ... A'(x) = 2 + 8*x + 40*x^2 + 544*x^3/3 + 2416*x^4/3 + 52864*x^5/15 + ... 1 + A(x)^4 = 2 + 8*x + 40*x^2 + 544*x^3/3 + 2416*x^4/3 + 52864*x^5/15 + ... 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^4-D[egf, x]], x], nmax]==ConstantArray[0, nmax]][[1]] PROG (PARI) {a(n) = local(A=1); A = 1 + serreverse( intformal( 1/(1 + (1+x)^4 +x*O(x^n)) )); n!*polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) \\ Paul D. Hanna, Jun 16 2015 CROSSREFS Cf. A000831, A258969, A258971, A258994, A258901. Sequence in context: A063528 A259705 A073561 * A230880 A214689 A202999 Adjacent sequences:  A258967 A258968 A258969 * A258971 A258972 A258973 KEYWORD nonn AUTHOR Vaclav Kotesovec, Jun 15 2015 STATUS approved

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Last modified April 20 01:20 EDT 2021. Contains 343117 sequences. (Running on oeis4.)