A336805 a(n) = (n!)^2 * Sum_{k=0..n} 3^(n-k) / (k!)^2.

1, 4, 49, 1324, 63553, 4766476, 514779409, 75672573124, 14529134039809, 3530579571673588, 1059173871502076401, 384480115355253733564, 166095409833469612899649, 84210372785569093740122044, 49515699197914627119191761873, 33423096958592373305454439264276, 25668938464198942698589009354963969

Offset: 0

Author

Ilya Gutkovskiy, Jan 27 2021

Keywords

• nonn

Crossrefs

Cf. A006040, A010845, A336804, A336807, A336808.

Programs

Mathematica

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

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (1 - 3*x).

a(0) = 1; a(n) = 3 * n^2 * a(n-1) + 1.