A320792 Number of multisets of exactly seven partitions of positive integers into distinct parts with total sum of parts equal to n.

1, 1, 3, 5, 11, 19, 37, 63, 114, 192, 331, 547, 914, 1482, 2412, 3847, 6126, 9620, 15052, 23292, 35889, 54806, 83294, 125658, 188656, 281418, 417828, 616838, 906516, 1325457, 1929644, 2796189, 4035315, 5798648, 8300214, 11833892, 16810048, 23790327, 33552202

Offset

7,3

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) = [x^n y^7] Product_{j>=1} 1/(1-y*x^j)^A000009(j).

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
      d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
    end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 8)
    end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..60);

Crossrefs

Column k=7 of A285229.

Cf. A000009.

Sequence in context: A175783 A078722 A320791 * A320793 A320794 A320795

Adjacent sequences: A320789 A320790 A320791 * A320793 A320794 A320795

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2018

Status

approved