A321777 Number of compositions of n into parts with distinct multiplicities and with exactly seven parts.

1, 7, 28, 42, 168, 238, 280, 428, 595, 595, 826, 910, 1078, 1232, 1716, 1498, 2023, 2093, 2450, 2450, 2996, 3228, 3626, 3710, 4193, 4263, 4998, 4928, 5916, 5838, 6426, 6510, 7371, 7455, 8316, 8464, 9198, 9268, 10318, 10248, 11319, 11473, 12524, 12460, 13636

Offset: 7

Author

Alois P. Heinz, Nov 18 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=7 of A242887.

Formula

Conjectures from Colin Barker, Dec 11 2018: (Start)

G.f.: x^7*(1 + 8*x + 36*x^2 + 78*x^3 + 245*x^4 + 475*x^5 + 719*x^6 + 1069*x^7 + 1419*x^8 + 1539*x^9 + 1645*x^10 + 1478*x^11 + 1100*x^12 + 708*x^13 + 505*x^14) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = -a(n-1) - a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) + 3*a(n-7) + 3*a(n-8) + 2*a(n-9) + a(n-10) - a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) - 2*a(n-15) - a(n-16) + a(n-18) + a(n-19) + a(n-20) + a(n-21) for n>27.

(End)