A258474 Number of partitions of n into two sorts of parts having exactly 4 parts of the second sort.

1, 6, 22, 63, 155, 342, 700, 1343, 2463, 4323, 7361, 12139, 19581, 30819, 47697, 72388, 108390, 159752, 232833, 334917, 477270, 672589, 940222, 1301954, 1790117, 2441168, 3308341, 4451294, 5955870, 7918574, 10475192, 13779096, 18042899, 23506156, 30496836

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..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(4, j)), j=0..n/i))), x, 5)
    end:
a:= n-> coeff(b(n$2), x, 4):
seq(a(n), n=4..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[4, j]}], {j, 0, n/i}]]], {x, 0, 5}];
a[n_] := Coefficient[b[n, n], x, 4];
a /@ Range[4, 40] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A256193.

Sequence in context: A166020 A307621 A257200 * A120477 A053739 A280481

Adjacent sequences: A258471 A258472 A258473 * A258475 A258476 A258477

Keyword

nonn

Author

Alois P. Heinz, May 31 2015

Status

approved