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A332508
a(n) = Sum_{d|n} binomial(n+d-2, n-1).
9
1, 3, 7, 25, 71, 280, 925, 3561, 12916, 49346, 184757, 710255, 2704157, 10427747, 40119781, 155288897, 601080391, 2334714319, 9075135301, 35352181116, 137846759282, 538302226628, 2104098963721, 8233718962365, 32247603703576, 126412458920775, 495918551104687
OFFSET
1,2
LINKS
FORMULA
a(n) = [x^n] Sum_{k>=1} x^k / (1 - x^k)^n.
a(n) ~ 4^(n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Aug 04 2022
MATHEMATICA
Table[DivisorSum[n, Binomial[n + # - 2, n - 1] &], {n, 1, 27}]
Table[SeriesCoefficient[Sum[x^k/(1 - x^k)^n, {k, 1, n}], {x, 0, n}], {n, 1, 27}]
PROG
(PARI) a(n) = sumdiv(n, d, binomial(n+d-2, n-1)); \\ Michel Marcus, Feb 14 2020
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 14 2020
STATUS
approved