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A277643
Partial sums of number of overpartitions (A015128).
4
1, 3, 7, 15, 29, 53, 93, 157, 257, 411, 643, 987, 1491, 2219, 3259, 4731, 6793, 9657, 13605, 19005, 26341, 36245, 49533, 67261, 90789, 121855, 162679, 216087, 285655, 375903, 492527, 642671, 835283, 1081539, 1395347, 1793987, 2298873, 2936465, 3739401, 4747849
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} A015128(k).
a(n) ~ exp(Pi*sqrt(n))/(4*Pi*sqrt(n)) * (1 + Pi/(4*sqrt(n))).
G.f.: 1/(1-x) * Product_{k>=1} (1 + x^k) / (1 - x^k). - Vaclav Kotesovec, Mar 25 2017
G.f.: 1/((1 - x)*theta_4(x)), where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 20 2018
MATHEMATICA
Accumulate[Table[Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 0, 50}]]
nmax = 50; CoefficientList[Series[1/(1-x) * Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 25 2016
STATUS
approved