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 A335501 a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} binomial(n,k)^2 * (n-k) * a(k). 0
 1, 2, 10, 86, 1098, 19142, 431926, 12150518, 414474570, 16781350694, 792845706630, 43107783435158, 2666346336398454, 185796230244565462, 14464057604306584774, 1248919312238777955086, 118855834572748011228490, 12397162719421869533115622 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = (n!)^2 * [x^n] exp(2 * Sum_{k>=1} x^k / (k!)^2). a(n) = (n!)^2 * [x^n] exp(2 * (BesselI(0,2*sqrt(x)) - 1)). MATHEMATICA a[0] = 1; a[n_] := a[n] = (2/n) Sum[Binomial[n, k]^2 (n - k) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}] nmax = 17; CoefficientList[Series[Exp[2 Sum[x^k/(k!)^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A001861, A023998. Sequence in context: A202745 A208833 A145082 * A295836 A245496 A185388 Adjacent sequences:  A335498 A335499 A335500 * A335502 A335503 A335504 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 12 2020 STATUS approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)