OFFSET
0,3
COMMENTS
Number of compositions (ordered partitions) of n into triangular numbers of n kinds.
LINKS
FORMULA
a(n) = [x^n] 1/(1 - n*Sum_{k>=1} x^(k*(k+1)/2)).
a(n) ~ n^n * (1 + 1/n - 3/(2*n^2) - 13/(3*n^3) + 181/(24*n^4) + 2251/(120*n^5) - 34949/(720*n^6) - 221539/(2520*n^7) + 13489169/(40320*n^8) + ...). - Vaclav Kotesovec, Mar 19 2018
MATHEMATICA
Table[SeriesCoefficient[1/(1 + n (1 - EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)))), {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[1/(1 - n Sum[x^(k (k + 1)/2), {k, 1, n}]), {x, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 18 2018
STATUS
approved