OFFSET
1,4
COMMENTS
Total number of parts in all partitions of n into distinct nonzero triangular numbers (A000217).
LINKS
FORMULA
G.f.: Sum_{i>=1} x^(i*(i+1)/2)/(1 + x^(i*(i+1)/2)) * Product_{j>=1} (1 + x^(j*(j+1)/2)).
EXAMPLE
a(10) = 4 because we have [10], [6, 3, 1] and 1 + 3 = 4.
MATHEMATICA
nmax = 90; Rest[CoefficientList[Series[Sum[x^(i (i + 1)/2)/(1 + x^(i (i + 1)/2)), {i, 1, nmax}] Product[1 + x^(j (j + 1)/2), {j, 1, nmax}], {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 26 2017
STATUS
approved