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 A337597 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 6^(k-1) * a(n-k). 6
 1, 1, 8, 96, 1896, 55416, 2182752, 111162528, 7088997888, 550749341952, 51058009732608, 5556160183592448, 699989463219105792, 100917906076208203776, 16486415052067886690304, 3026039346413717945757696, 619431153899977856767131648, 140491838894751995366936641536, 35102748598142373142198776889344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Robert Israel, Table of n, a(n) for n = 0..200 FORMULA Sum_{n>=0} a(n) * x^n / (n!)^2 = exp((BesselI(0,2*sqrt(6*x)) - 1) / 6). Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(Sum_{n>=1} 6^(n-1) * x^n / (n!)^2). MAPLE S:= series(exp((BesselI(0, 2*sqrt(6*x))-1)/6), x, 51): seq(coeff(S, x, j)*(j!)^2, j=0..50); # Robert Israel, Sep 06 2020 MATHEMATICA a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}] nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[6 x]] - 1)/6], {x, 0, nmax}], x] Range[0, nmax]!^2 CROSSREFS Cf. A005012, A337592, A337593, A337594, A337595. Sequence in context: A002168 A114425 A224767 * A052127 A300474 A338571 Adjacent sequences:  A337594 A337595 A337596 * A337598 A337599 A337600 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Sep 02 2020 STATUS approved

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Last modified May 26 02:45 EDT 2022. Contains 354074 sequences. (Running on oeis4.)