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A372513
Sum_{n>=0} a(n) * x^n / (n!)^2 = -log(BesselJ(0,2*sqrt(2*x))) / 2.
0
0, 1, 2, 16, 264, 7296, 302720, 17587200, 1362399360, 135693537280, 16893684928512, 2570631845806080, 469393033744588800, 101294080603625226240, 25502237392032633323520, 7408331513180811911233536, 2459543337577081650719784960, 925435622656059412145504256000
OFFSET
0,3
FORMULA
a(0) = 0; a(n) = (-2)^(n-1) - (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * (-2)^k * (n-k) * a(n-k).
a(n) = 2^(n-1) * A002190(n).
MATHEMATICA
nmax = 17; CoefficientList[Series[-Log[BesselJ[0, 2 Sqrt[2 x]]]/2, {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 0; a[n_] := a[n] = (-2)^(n - 1) - (1/n) Sum[Binomial[n, k]^2 (-2)^k (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]
CROSSREFS
Cf. A002190.
Sequence in context: A304317 A351918 A326272 * A283685 A197458 A050974
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 04 2024
STATUS
approved