A265096 a(n) = Sum_{k=0..n} p(k)*q(k), where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).

1, 2, 4, 10, 20, 41, 85, 160, 292, 532, 952, 1624, 2779, 4597, 7567, 12319, 19711, 30997, 48707, 75167, 115295, 175487, 264665, 395185, 587335, 865371, 1267311, 1845231, 2670627, 3839267, 5498051, 7824331, 11080441, 15624505, 21927225, 30633780, 42642416

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Formula

a(n) ~ (sqrt(2)-1) * exp((1+sqrt(2))*Pi*sqrt(n/3)) / (8*3^(1/4)*Pi*n^(5/4)).

Mathematica

Table[Sum[PartitionsQ[k]*PartitionsP[k], {k, 0, n}], {n, 0, 50}]

Crossrefs

Cf. A000009, A000041, A000070, A015128, A036469.

Partial sums of A304991.

Sequence in context: A189585 A239346 A004647 * A236572 A283213 A283251

Adjacent sequences: A265093 A265094 A265095 * A265097 A265098 A265099

Keyword

nonn

Author

Vaclav Kotesovec, Dec 01 2015

Status

approved