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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
Eric Weisstein's World of Mathematics, Triangular Number
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
Sequence in context: A321664 A250099 A241949 * A214720 A035368 A249686
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 05 2017
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)