A293464 a(n) = Sum_{k=0..n} (-1)^k * 2^k * p(k), where p(k) is the partition function A000041.

1, -1, 7, -17, 63, -161, 543, -1377, 4255, -11105, 31903, -82785, 232607, -594785, 1617055, -4150113, 10988703, -27939681, 72985759, -183915361, 473541791, -1187402593, 3015290015, -7512413025, 18911702175, -46787875681, 116689317023, -287306044257

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

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

a(n) ~ (-1)^n * 2/3 * 2^n * A000041(n).

Mathematica

Table[Sum[(-1)^k * 2^k * PartitionsP[k], {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A087787, A259400.

Sequence in context: A262106 A081632 A276907 * A106010 A136192 A269239

Adjacent sequences: A293461 A293462 A293463 * A293465 A293466 A293467

Keyword

sign

Author

Vaclav Kotesovec, Oct 09 2017

Status

approved