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

0,4

Links

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

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 *)

Crossrefs

Main diagonal of A175804.

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

Sequence in context: A046745 A390563 A198950 * A015902 A301427 A300275

Adjacent sequences: A379375 A379376 A379377 * A379379 A379380 A379381

Keyword

nonn

Author

Alois P. Heinz, Dec 21 2024

Status

approved