A352467 a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k)^2 * a(n-k).

1, 1, 37, 8551, 6886069, 14323022551, 64085654997739, 545107167737695109, 8062740187879748199029, 193866963305030079530064391, 7188682292472952994057436691387, 394013888612808806428687953794890229, 30829606055995735731623164115609901072859

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

Sum_{n>=0} a(n) * x^(2*n) / (2*n)!^2 = 1 / (1 - Sum_{n>=1} x^(2*n) / (2*n)!^2).

Sum_{n>=0} a(n) * x^(2*n) / (2*n)!^2 = 1 / (2 - (BesselI(0,2*sqrt(x)) + BesselJ(0,2*sqrt(x))) / 2).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n, 2 k]^2 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 12}]
nmax = 24; Take[CoefficientList[Series[1/(1 - Sum[x^(2 k)/(2 k)!^2, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^2, {1, -1, 2}]

Crossrefs

Cf. A094088, A102221, A352468, A352470.

Sequence in context: A219105 A219984 A083117 * A219001 A212945 A220811

Adjacent sequences: A352464 A352465 A352466 * A352468 A352469 A352470

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2022

Status

approved