OFFSET
28,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 28..1000
FORMULA
a(n) = n! * [x^n*y^7] Product_{n>=1} (1+y*x^n/n!).
MAPLE
b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n, i))))
end:
a:= n-> b(n$2, 7):
seq(a(n), n=28..40);
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[t > i || t*(t + 1)/2 > n || t*(2*i + 1 - t)/2 < n, 0, If[n == 0, 1, b[n, i - 1, t] + If[i > n, 0, b[n - i, i - 1, t - 1]*Binomial[n, i]]]];
a[n_] := b[n, n, 7];
Table[a[n], {n, 28, 40}] (* Jean-François Alcover, May 24 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 01 2016
STATUS
approved