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

0,2

Links

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

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

Cf. A015128, A000070, A036469, A026906.

Cf. A211971, A002865, A087897.

Sequence in context: A009859 A322108 A182640 * A192960 A182717 A122768

Adjacent sequences: A277640 A277641 A277642 * A277644 A277645 A277646

Keyword

nonn

Author

Vaclav Kotesovec, Oct 25 2016

Status

approved