OFFSET
0,6
FORMULA
G.f.: Sum_{k>=1} k! * x^(k*(k + 3)/2) / Product_{j=1..k-1} (1 - x^j).
EXAMPLE
a(9) = 8 because we have [7, 2], [4, 3, 2], [4, 2, 3], [3, 4, 2], [3, 2, 4], [2, 7], [2, 4, 3] and [2, 3, 4].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-2)*(i+3)/2<n, 0,
add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
end:
a:= n-> `if`(n<2, 0, b(n-2$2, 1)):
seq(a(n), n=0..55); # Alois P. Heinz, Nov 25 2020
MATHEMATICA
nmax = 47; CoefficientList[Series[Sum[k! x^(k (k + 3)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 25 2020
STATUS
approved