OFFSET
0,14
FORMULA
G.f.: Sum_{k>=0} k! * x^(k*(k + 11)/2) / Product_{j=1..k} (1 - x^j).
EXAMPLE
a(13) = 3 because we have [13], [7, 6] and [6, 7].
MAPLE
b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`((i-5)*(i+6)/2<n, 0,
add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60); # Alois P. Heinz, Nov 23 2020
MATHEMATICA
nmax = 57; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 23 2020
STATUS
approved