A277643 Partial sums of number of overpartitions (A015128).

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

Author

Vaclav Kotesovec, Oct 25 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A015128, A000070, A036469, A026906.

Cf. A211971, A002865, A087897.

Programs

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 *)

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