cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A309670 Number of colored compositions of n using all colors of an initial interval of the color palette such that all parts have different color patterns and the patterns for parts i are sorted and have i colors in (weakly) increasing order.

Original entry on oeis.org

1, 1, 3, 21, 115, 813, 7627, 71173, 740023, 8544169, 107195083, 1434581205, 20499413667, 312262663989, 4992164670007, 84221279919193, 1492818584618099, 27607818180267269, 533522844488072987, 10724970103003953053, 223859943086157531063, 4847766598150865273721
Offset: 0

Views

Author

Alois P. Heinz, Sep 18 2019

Keywords

Crossrefs

Row sums of A327244.

Programs

  • Maple
    C:= binomial:
    b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
          b(n-i*j, min(n-i*j, i-1), k, p+j)/j!*C(C(k+i-1, i), j), j=0..n/i)))
        end:
    a:= n-> add(add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
    seq(a(n), n=0..23);
  • Mathematica
    c = Binomial;
    b[n_, i_, k_, p_] := b[n, i, k, p] = If[n == 0, p!, If[i<1, 0, Sum[b[n - i*j, Min[n - i*j, i-1], k, p+j]/j!*c[c[k+i-1, i], j], {j, 0, n/i}]]];
    a[n_] := Sum[Sum[b[n, n, i, 0]*(-1)^(k-i)*c[k, i], {i, 0, k}], {k, 0, n}];
    Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Mar 05 2022, after Alois P. Heinz *)