|
|
A288126
|
|
Number of partitions of n-th triangular number (A000217) into distinct triangular parts.
|
|
10
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
a(n) = [x^(n*(n+1)/2)] Product_{k>=1} (1 + x^(k(k+1)/2)).
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|