OFFSET
0,2
COMMENTS
Number of partitions of n into odd parts with n + 1 kinds of 1.
FORMULA
a(n) = [x^n] (1/(1 - x)^n)*Product_{k>=1} 1/(1 - x^(2*k-1)).
a(n) = [x^n] (1/(1 - x)^n)*exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))).
a(n) ~ QPochhammer[-1, 1/2] * 4^(n-1) / sqrt(Pi*n). - Vaclav Kotesovec, May 18 2018
MATHEMATICA
Table[SeriesCoefficient[1/(1 - x)^n Product[(1 + x^k), {k, 1, n}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[1/(1 - x)^n Product[1/(1 - x^(2 k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[1/(1 - x)^n Exp[Sum[(-1)^(k + 1) x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[QPochhammer[-1, x]/(2 (1 - x)^n), {x, 0, n}], {n, 0, 26}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 18 2018
STATUS
approved