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A336242 a(n) = (n!)^2 * Sum_{d|n} (-1)^(d+1) / (d!)^2. 1
1, 3, 37, 431, 14401, 403199, 25401601, 1216454399, 135339724801, 9877056537599, 1593350922240001, 178056522962841599, 38775788043632640001, 5700041141609893478399, 1757631343928533032960001, 327562346808114783805439999, 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} (1 - BesselJ(0,2*x^(k/2))).

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

MATHEMATICA

Table[(n!)^2 Sum[(-1)^(d + 1)/(d!)^2, {d, Divisors[n]}], {n, 1, 17}]

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

PROG

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

CROSSREFS

Cf. A073701, A132958, A336241.

Sequence in context: A183960 A338717 A346952 * A054596 A155667 A216696

Adjacent sequences:  A336239 A336240 A336241 * A336243 A336244 A336245

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 13 2020

STATUS

approved

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Last modified May 26 11:30 EDT 2022. Contains 354086 sequences. (Running on oeis4.)