A318250 a(n) = (n - 1)! * sigma_2(n), where sigma_2(n) = sum of squares of divisors of n (A001157).

1, 5, 20, 126, 624, 6000, 36000, 428400, 3669120, 47174400, 442713600, 8382528000, 81430272000, 1556755200000, 22666355712000, 445916959488000, 6067609067520000, 161837779783680000, 2317659281473536000, 66418224823222272000, 1216451004088320000000, 31165474724742758400000

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

E.g.f.: Sum_{k>=1} x^k/(k*(1 - x^k)^2).

E.g.f.: -log(Product_{k>=1} (1 - x^k)^k).

E.g.f.: A(x) = log(B(x)), where B(x) = o.g.f. of A000219.

a(p^k) = (p^(2*k+2) - 1)*(p^k - 1)!/(p^2 - 1), where p is a prime.

Mathematica

Table[(n - 1)! DivisorSigma[2, n], {n, 1, 22}]
nmax = 22; Rest[CoefficientList[Series[Sum[x^k/(k (1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
nmax = 22; Rest[CoefficientList[Series[-Log[Product[(1 - x^k)^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!]

Prog

(PARI) a(n) = (n-1)!*sigma(n, 2); \\ Michel Marcus, Aug 22 2018

Crossrefs

Cf. A000219, A001157, A038048, A318249.

Sequence in context: A301952 A110373 A081067 * A337292 A024066 A009569

Adjacent sequences: A318247 A318248 A318249 * A318251 A318252 A318253

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 22 2018

Status

approved