A336241 a(n) = (n!)^2 * Sum_{d|n} 1 / (d!)^2.

1, 5, 37, 721, 14401, 662401, 25401601, 2034950401, 135339724801, 16461151257601, 1593350922240001, 293575350020198401, 38775788043632640001, 9500068369885892198401, 1757631343928533032960001, 547963926586675321282560001, 126513546505547170185216000001

Offset: 1

Author

Ilya Gutkovskiy, Jul 13 2020

Keywords

• nonn

Crossrefs

Cf. A006040, A057625, A336242.

Programs

Mathematica

Table[(n!)^2 Sum[1/(d!)^2, {d, Divisors[n]}], {n, 1, 17}]
nmax = 17; CoefficientList[Series[Sum[(BesselI[0, 2 x^(k/2)] - 1), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2 // Rest

PARI

a(n) = n!^2*sumdiv(n, d, 1/d!^2); \\ Michel Marcus, Jul 13 2020

Formula

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

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