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%I #7 Jul 13 2020 22:20:57
%S 1,5,37,721,14401,662401,25401601,2034950401,135339724801,
%T 16461151257601,1593350922240001,293575350020198401,
%U 38775788043632640001,9500068369885892198401,1757631343928533032960001,547963926586675321282560001,126513546505547170185216000001
%N a(n) = (n!)^2 * Sum_{d|n} 1 / (d!)^2.
%F a(n) = (n!)^2 * [x^n] Sum_{k>=1} (BesselI(0,2*x^(k/2)) - 1).
%F a(n) = (n!)^2 * [x^n] Sum_{k>=1} x^k / ((k!)^2 * (1 - x^k)).
%t Table[(n!)^2 Sum[1/(d!)^2, {d, Divisors[n]}], {n, 1, 17}]
%t nmax = 17; CoefficientList[Series[Sum[(BesselI[0, 2 x^(k/2)] - 1), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2 // Rest
%o (PARI) a(n) = n!^2*sumdiv(n, d, 1/d!^2); \\ _Michel Marcus_, Jul 13 2020
%Y Cf. A006040, A057625, A336242.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Jul 13 2020
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