A288126 Number of partitions of n-th triangular number (A000217) into distinct triangular parts.

1, 1, 1, 1, 2, 1, 2, 3, 2, 4, 7, 6, 4, 14, 15, 19, 31, 28, 43, 57, 80, 103, 127, 181, 234, 295, 398, 539, 663, 888, 1178, 1419, 1959, 2519, 3102, 4201, 5282, 6510, 8717, 11162, 13557, 18108, 22965, 28206, 36860, 46350, 58060, 73857, 93541, 117058, 147376, 186158, 232949, 292798, 365639

Offset: 0

Author

Ilya Gutkovskiy, Jun 05 2017

Keywords

• nonn

Examples

			a(4) = 2 because 4th triangular number is 10 and we have [10], [6, 3, 1].
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Triangular Number
• Index to sequences related to polygonal numbers
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000217, A007294, A024940, A030273, A037444, A072964.

Programs

Maple

N:= 100:
G:= mul(1+x^(k*(k+1)/2),k=1..N):
seq(coeff(G,x,n*(n+1)/2),n=0..N); # Robert Israel, Jun 06 2017

Mathematica

Table[SeriesCoefficient[Product[1 + x^(k (k + 1)/2), {k, 1, n}], {x, 0, n (n + 1)/2}], {n, 0, 54}]

Formula

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

a(n) = A024940(A000217(n)).