A293467 a(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) * q(k), where q(k) is A000009 (partitions into distinct parts).

1, 0, 0, -1, -3, -7, -14, -25, -41, -64, -100, -165, -294, -550, -1023, -1795, -2823, -3658, -2882, 2873, 20435, 62185, 148863, 314008, 613957, 1155794, 2175823, 4244026, 8753538, 19006490, 42471787, 95234575, 210395407, 453413866, 949508390, 1931939460

Offset: 0

Author

Vaclav Kotesovec, Oct 09 2017

Keywords

• sign

Comments

Multiply by (-1)^n to get A380412, which is the first term of the n-th differences of the strict partition numbers, or column n=0 of A378622. - Gus Wiseman, Feb 04 2025

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• Vaclav Kotesovec, Graph: a(n)/2^n (40000 terms)

Crossrefs

Cf. A025147, A266232, A294467, A294468.

Cf. A218481, A294466, A095051.

The non-strict version is the absolute value of A281425; see A175804, A320590.

Up to sign, same as A380412. See A320591, A377285, A378970, A378971.

A000009 counts strict integer partitions, differences A087897.

Cf. A000041, A002865, A007442, A008284, A116608.

Programs

Mathematica

Table[Sum[(-1)^k * Binomial[n, k] * PartitionsQ[k], {k, 0, n}], {n, 0, 50}]