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

0,5

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

Formula

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

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

Example

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

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}]

Crossrefs

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

Sequence in context: A321664 A250099 A241949 * A214720 A035368 A249686

Adjacent sequences: A288123 A288124 A288125 * A288127 A288128 A288129

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 05 2017

Status

approved