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A340955
Number of ways to write n as an ordered sum of 10 nonzero triangular numbers.
9
1, 0, 10, 0, 45, 10, 120, 90, 210, 370, 297, 930, 570, 1620, 1480, 2220, 3375, 2940, 6085, 4590, 8981, 8370, 11430, 15100, 13890, 23832, 19155, 31940, 30195, 38520, 46890, 46440, 66550, 59400, 86355, 81532, 104220, 114390, 122410, 153450, 149490, 193440, 188010, 235350, 238840
OFFSET
10,3
LINKS
FORMULA
G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^10, where theta_2() is the Jacobi theta function.
MAPLE
b:= proc(n, k) option remember; local r, t, d; r, t, d:= $0..2;
if n=0 then `if`(k=0, 1, 0) else
while t<=n do r:= r+b(n-t, k-1); t, d:= t+d, d+1 od; r fi
end:
a:= n-> b(n, 10):
seq(a(n), n=10..54); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 54; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^10, {x, 0, nmax}], x] // Drop[#, 10] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved