A246231 Number of compositions of n into exactly four different parts with distinct multiplicities.

12600, 78120, 189000, 549000, 1389960, 2858640, 6471699, 15289662, 29639082, 64025820, 134997382, 267550925, 545274648, 1161661901, 2223888268, 4552401195, 9185643748, 17829746962, 35102264675, 71613947350, 135793314152, 270167493481, 534784841445

Offset: 20

Author

Alois P. Heinz, Aug 19 2014

Keywords

• nonn

Links

• Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 20..220 (first 120 terms from Alois P. Heinz)

Crossrefs

Column k=4 of A242896.

Programs

Mathematica

b[n_, i_, s_List] := b[n, i, s] = If[n == 0, Total[s]!, If[i<1, 0, Expand[ Sum[ If[j>0 && MemberQ[s, j], 0, If[j == 0, 1, x]*b[n-i*j, i-1, If[j == 0, s, s ~Union~ {j}]]/j!], {j, 0, n/i}]]]]; a[n_] := Coefficient[b[n, n, {}], x, 4]; Table[a[n], {n, 20, 50}] (* Jean-François Alcover, Feb 11 2015, after Alois P. Heinz *)