A340886 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 2^(n-k-1) * a(k).

1, 1, 6, 76, 1720, 60816, 3096384, 214579296, 19422473088, 2224980891904, 314675568756736, 53849929134122496, 10966912240761425920, 2621246193301011159040, 726608751113679704248320, 231217063994112487051984896, 83713709650818121936828858368

Offset

0,3

Links

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

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = 2 / (3 - BesselI(0,2*sqrt(2*x))).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 2^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[2/(3 - BesselI[0, 2 Sqrt[2 x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A102221, A122704, A340887, A340888.

Sequence in context: A218303 A132613 A009763 * A305999 A274464 A028979

Adjacent sequences: A340883 A340884 A340885 * A340887 A340888 A340889

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 25 2021

Status

approved