A380412 First term of the n-th differences of the strict partition numbers. Inverse zero-based binomial transform of A000009.

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

Gus Wiseman, Feb 03 2025

Keywords

• sign

Comments

Up to sign, same as A293467.

Crossrefs

The version for non-strict partitions is A281425, row n=0 of A175804.

Column n=0 of A378622.

A000009 counts strict integer partitions, differences A087897, A378972.

A266232 gives zero-based binomial transform of A000009, differences A129519.

Cf. A000041, A007442, A008284, A218482, A293467, A320590, A320591, A377285, A378970.

Programs

Mathematica

nn=10;Table[First[Differences[PartitionsQ/@Range[0,nn],n]],{n,0,nn}]

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) binomial(n,k) A000041(k).