A340888 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 4^(n-k-1) * a(k).

1, 1, 8, 124, 3456, 150656, 9453056, 807373568, 90066059264, 12716049596416, 2216452086693888, 467465806422867968, 117332539562036035584, 34562989958399757647872, 11807922834511544081973248, 4630865359842075866336067584, 2066370767828213666946077425664

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = 4 / (5 - BesselI(0,4*sqrt(x))).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 4^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[4/(5 - BesselI[0, 4 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A102221, A326324, A340886, A340887.

Sequence in context: A254125 A371298 A024282 * A231638 A065082 A053058

Adjacent sequences: A340885 A340886 A340887 * A340889 A340890 A340891

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 25 2021

Status

approved