A298858 Number of ordered ways of writing n-th triangular number as a sum of n nonzero triangular numbers.

1, 1, 0, 0, 4, 11, 86, 777, 4670, 36075, 279482, 2345201, 21247326, 197065752, 1983741228, 20769081251, 228078253168, 2604226354265, 30880251148086, 379415992755572, 4818158748326064, 63116999199457944, 851467484377802094, 11811530978240316682, 168243449082524484856

Offset: 0

Author

Ilya Gutkovskiy, Jan 27 2018

Keywords

• nonn

Examples

			a(4) = 4 because fourth triangular number is 10 and we have [3, 3, 3, 1], [3, 3, 1, 3], [3, 1, 3, 3] and [1, 3, 3, 3].
		

Links

• Eric Weisstein's World of Mathematics, Triangular Number
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000217, A007294, A023361, A024940, A072964, A106337, A196010, A288126, A298329, A298330.

Programs

Mathematica

Table[SeriesCoefficient[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^n, {x, 0, n (n + 1)/2}], {n, 0, 24}]

Formula

a(n) = [x^(n*(n+1)/2)] (Sum_{k>=1} x^(k*(k+1)/2))^n.