A258475 Number of partitions of n into two sorts of parts having exactly 5 parts of the second sort.

1, 7, 29, 92, 247, 590, 1291, 2642, 5114, 9475, 16882, 29159, 48914, 80160, 128405, 201958, 311878, 474540, 711222, 1052949, 1539214, 2226774, 3186866, 4520230, 6351925, 8856519, 12248350, 16822982, 22940863, 31092121, 41871405, 56078299, 74676693, 98949447

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
      `if`(i<1, 0, add(b(n-i*j, i-1)*add(x^t*
       binomial(j, t), t=0..min(5, j)), j=0..n/i))), x, 6)
    end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=5..40);

Mathematica

b[n_, i_] := b[n, i] = Series[If[n==0, 1, If[i<1, 0, Sum[b[n-i*j, i-1]*Sum[ x^t*Binomial[j, t], {t, 0, Min[5, j]}], {j, 0, n/i}]]], {x, 0, 6}];
a[n_] := Coefficient[b[n, n], x, 5];
a /@ Range[5, 40] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A256193.

Sequence in context: A166189 A001779 A257201 * A320753 A053295 A266939

Adjacent sequences: A258472 A258473 A258474 * A258476 A258477 A258478

Keyword

nonn

Author

Alois P. Heinz, May 31 2015

Status

approved