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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
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 28 2020
STATUS
approved