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A072964
Number of partitions of n-th triangular number n(n+1)/2 (A000217(n)) into triangular parts.
16
1, 1, 2, 4, 7, 15, 32, 66, 141, 295, 619, 1286, 2654, 5460, 11066, 22357, 44962, 89258, 176459, 347103, 675846, 1309903, 2525893, 4830943, 9196093, 17418788, 32772432, 61375543, 114401182, 212026732, 391231769, 718710706, 1313781686
OFFSET
0,3
COMMENTS
What is limit_{n->inf} a(n)^(1/n)? [This limit is equal to 1. - Vaclav Kotesovec, May 21 2018]
FORMULA
a(n) = A007294[n(n+1)/2] = coefficient of x^[n(n+1)/2] in the expansion of product_{k=1..inf} 1/(1 - x^(k(k+1)/2)).
a(n) = A007294(A000217(n)).
a(n) ~ exp(3*Pi^(1/3) * Zeta(3/2)^(2/3) * (n*(n+1))^(1/3) / 2^(4/3)) * Zeta(3/2) / (4*Pi*sqrt(3)*n^3). - Vaclav Kotesovec, May 21 2018
MATHEMATICA
c = CoefficientList[ Series[1/Product[1 - x^(i(i + 1)/2), {i, 1, 50}], {x, 0, 565}], x]; c[[Range[33]*(Range[33] + 1)/2 + 1]] (* Robert G. Wilson v *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 13 2002
EXTENSIONS
Entry revised by N. J. A. Sloane, Jan 28 2007
STATUS
approved