A259436 a(n) = Sum_{k=0..n} p(k)^k, where p(k) is the partition function A000041.

1, 2, 6, 33, 658, 17465, 1789026, 172648401, 55048521937, 19738048521937, 17099936170199761, 17002207325552593617, 43456890729289136241538, 113852784934058230923022839, 667954362620824922543667163464, 4816707198961510396593071163584840

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ p(n)^n ~ exp(1/24 - 3/(4*Pi^2) - (72+Pi^2)*sqrt(n)/(24*sqrt(6)*Pi) + sqrt(2/3)*Pi*n^(3/2)) / (3^(n/2) * 4^n * n^n).

Mathematica

Table[Sum[PartitionsP[k]^k, {k, 0, n}], {n, 0, 15}]

Crossrefs

Cf. A000041, A133018, A259373, A259399, A259437, A259438, A265095.

Sequence in context: A012874 A005161 A062970 * A278611 A088125 A064940

Adjacent sequences: A259433 A259434 A259435 * A259437 A259438 A259439

Keyword

nonn

Author

Vaclav Kotesovec, Jun 27 2015

Status

approved