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 A364398 G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)). 5
 1, 2, -14, 162, -2270, 35234, -582958, 10076354, -179802046, 3287029698, -61246957902, 1158889656930, -22207636788894, 430106644358242, -8405699952109166, 165557885912786818, -3282954949273886590, 65487784219460233602, -1313225110482709157518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..18. FORMULA a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(4*n+k-2,n-1) for n > 0. D-finite with recurrence 2*n*(462919*n -714364)*(4*n-3) *(2*n-1)*(4*n-1)*a(n) +(625365036*n^5 -2723245780*n^4 +4202103460*n^3 -2471353250*n^2 +81675089*n +289227120)*a(n-1) +(-484851248*n^5 +5501638270*n^4 -25122933600*n^3 +57439557800*n^2 -65490996232*n +29691239955)*a(n-2) +(2*n-5)*(652184*n -1103659)*(4*n-13) *(n-3)*(4*n-11)*a(n-3)=0. - R. J. Mathar, Jul 25 2023 a(n) ~ c*(-1)^(n-1)*256^n*27^(-n)*2F1([1-n, 4*n], [3*n], -1)*n^(-3/2), with c = sqrt(3/(32*Pi)). - Stefano Spezia, Oct 21 2023 MAPLE A364398 := proc(n) if n = 0 then 1; else (-1)^(n-1)*add( binomial(n, k) * binomial(4*n+k-2, n-1), k=0..n)/n ; end if; end proc: seq(A364398(n), n=0..70); # R. J. Mathar, Jul 25 2023 MATHEMATICA nmax = 18; A[_] = 1; Do[A[x_] = 1+x/A[x]^3*(1+1/A[x]) + O[x]^(nmax+1) // Normal, {nmax}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 21 2023 *) PROG (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(4*n+k-2, n-1))/n); CROSSREFS Cf. A112478, A364394, A364396. Cf. A364399, A364400. Cf. A260332. Sequence in context: A268011 A052112 A354241 * A074635 A201465 A245894 Adjacent sequences: A364395 A364396 A364397 * A364399 A364400 A364401 KEYWORD sign AUTHOR Seiichi Manyama, Jul 22 2023 STATUS approved

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Last modified November 29 07:03 EST 2023. Contains 367429 sequences. (Running on oeis4.)