OFFSET
0,7
COMMENTS
Number of partitions of n into nonzero 4-dimensional pyramidal numbers (A002415).
LINKS
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)^2*(k+2)/12)).
EXAMPLE
a(12) = 3 because we have [6, 6], [6, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
MAPLE
N:= 100: # for a(0)..a(N)
P:= 1:
for k from 1 do
e:= k*(k+1)^2*(k+2)/12;
if e > N then break fi;
P:= P/(1-x^e);
od:
S:= series(P, x, N+1):
[seq](coeff(S, x, n), n=0..N); # Robert Israel, Aug 28 2019
MATHEMATICA
nmax = 90; CoefficientList[Series[Product[1/(1 - x^(k (k + 1)^2 (k + 2)/12)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 15 2017
STATUS
approved