A379378 The n-th term of the n-th forward differences of partition numbers A000041.

1, 1, 1, 2, 5, 10, 22, 64, 159, 328, 747, 1914, 4608, 10252, 23339, 55405, 128034, 287855, 660549, 1541383, 3528645, 7921187, 17870633, 40689873, 92248847, 207911243, 469331387, 1059603243, 2377923972, 5313383490, 11889346697, 26641635997, 59560543885

Offset: 0

Author

Alois P. Heinz, Dec 21 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3209

Crossrefs

Main diagonal of A175804.

Cf. A000041, A033815, A281425, A386457 (parity).

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0,
      combinat[numbpart](n), b(n+1, k-1)-b(n, k-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..32);

Mathematica

A379378list[nmax_] := Module[{p = PartitionsP[Range[0, nmax*2]]}, Join[{First[p]}, Table[First[p = Differences[Rest[p]]], nmax]]];
A379378list[50] (* Paolo Xausa, Jul 26 2025 *)