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A336638
Sum_{n>=0} a(n) * x^n / (n!)^2 = 1 / BesselJ(0,2*sqrt(x))^3.
3
1, 3, 21, 255, 4725, 123903, 4368729, 199467243, 11455187445, 808475761695, 68805857523321, 6950458374996843, 822292004658568761, 112639503374757412875, 17688916392275574761805, 3157133540377493872350855, 635546443798928578953138165
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k)^2 * A002893(k) * a(n-k).
MATHEMATICA
nmax = 16; CoefficientList[Series[1/BesselJ[0, 2 Sqrt[x]]^3, {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k]^2 HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
CROSSREFS
Column k=3 of A340986.
Sequence in context: A209917 A179504 A197716 * A317059 A262939 A232470
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 28 2020
STATUS
approved