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

0,5

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Triangular Number

Index to sequences related to polygonal numbers

Formula

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

Example

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].

Mathematica

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

Crossrefs

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

Sequence in context: A000850 A004796 A320289 * A181267 A280036 A125888

Adjacent sequences: A298855 A298856 A298857 * A298859 A298860 A298861

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Jan 27 2018

Status

approved