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 A336635 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^2 - 1). 2
 1, 2, 14, 176, 3470, 96792, 3590048, 169686792, 9903471502, 696692504552, 57958925154584, 5614276497440712, 625153195794408608, 79159558899671117896, 11293672011942106846808, 1801015209162807119535216, 318805481931592799427378062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * binomial(2*k,k) * k * a(n-k). MATHEMATICA nmax = 16; CoefficientList[Series[Exp[BesselI[0, 2 Sqrt[x]]^2 - 1], {x, 0, nmax}], x] Range[0, nmax]!^2 a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 Binomial[2 k, k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}] CROSSREFS Cf. A000984, A023998, A055882, A323666, A336636, A336637. Sequence in context: A233224 A167014 A300282 * A352761 A208195 A252727 Adjacent sequences: A336632 A336633 A336634 * A336636 A336637 A336638 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 28 2020 STATUS approved

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Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)