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A336241 a(n) = (n!)^2 * Sum_{d|n} 1 / (d!)^2. 1
1, 5, 37, 721, 14401, 662401, 25401601, 2034950401, 135339724801, 16461151257601, 1593350922240001, 293575350020198401, 38775788043632640001, 9500068369885892198401, 1757631343928533032960001, 547963926586675321282560001, 126513546505547170185216000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..17.

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)).

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

PROG

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

CROSSREFS

Cf. A006040, A057625, A336242.

Sequence in context: A121834 A215233 A083846 * A180275 A257952 A240186

Adjacent sequences:  A336238 A336239 A336240 * A336242 A336243 A336244

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 13 2020

STATUS

approved

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Last modified May 26 02:45 EDT 2022. Contains 354074 sequences. (Running on oeis4.)