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A336635 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^2 - 1). 2

%I

%S 1,2,14,176,3470,96792,3590048,169686792,9903471502,696692504552,

%T 57958925154584,5614276497440712,625153195794408608,

%U 79159558899671117896,11293672011942106846808,1801015209162807119535216,318805481931592799427378062

%N Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^2 - 1).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * binomial(2*k,k) * k * a(n-k).

%t nmax = 16; CoefficientList[Series[Exp[BesselI[0, 2 Sqrt[x]]^2 - 1], {x, 0, nmax}], x] Range[0, nmax]!^2

%t 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}]

%Y Cf. A000984, A023998, A055882, A323666, A336636, A336637.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Jul 28 2020

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Last modified January 30 07:12 EST 2023. Contains 359939 sequences. (Running on oeis4.)