A320569 a(n) = [x^n] exp(Sum_{k>=1} sigma_n(k)*x^k/(k*(1 - x)^k)).

1, 1, 4, 25, 272, 5028, 173754, 11639691, 1488266409, 375932630887, 190981026883402, 191456188687238845, 388595050299100664773, 1602566853459119962711220, 13153292027392201138778117308, 220500920265786114712328027650814, 7523329040995438987558888118224263531

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = [x^n] Product_{k>=1} 1/(1 - x^k/(1 - x)^k)^(k^(n-1)).

Maple

seq(coeff(series(mul((1-x^k/(1-x)^k)^(-k^(n-1)), k=1..n), x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 15 2018

Mathematica

Table[SeriesCoefficient[Exp[Sum[DivisorSigma[n, k] x^k/(k (1 - x)^k), {k, 1, n}]], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[Product[1/(1 - x^k/(1 - x)^k)^(k^(n - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 16}]

Crossrefs

Cf. A218482, A319361, A320563.

Sequence in context: A308008 A144281 A361589 * A058791 A216660 A352859

Adjacent sequences: A320566 A320567 A320568 * A320570 A320571 A320572

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 15 2018

Status

approved