A336808 a(n) = (n!)^2 * Sum_{k=0..n} 5^(n-k) / (k!)^2.

1, 6, 121, 5446, 435681, 54460126, 9802822681, 2401691556846, 768541298190721, 311259225767242006, 155629612883621003001, 94155915794590706815606, 67792259372105308907236321, 57284459169428986026614691246, 56138769986040406306082397421081, 63156116234295457094342697098716126

Offset: 0

Author

Ilya Gutkovskiy, Jan 27 2021

Keywords

• nonn

Crossrefs

Cf. A006040, A056546, A336804, A336805, A336807.

Programs

Mathematica

Table[n!^2 Sum[5^(n - k)/k!^2, {k, 0, n}], {n, 0, 15}]
nmax = 15; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 5 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 - 5*x).

a(0) = 1; a(n) = 5 * n^2 * a(n-1) + 1.