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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS What is limit_{n->inf} a(n)^(1/n)? [This limit is equal to 1. - Vaclav Kotesovec, May 21 2018] LINKS T. D. Noe, Table of n, a(n) for n=0..100 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 Cf. A007294, A073420, A114738. Sequence in context: A049885 A129682 A129981 * A247291 A030033 A280031 Adjacent sequences:  A072961 A072962 A072963 * A072965 A072966 A072967 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 13 2002 EXTENSIONS Entry revised by N. J. A. Sloane, Jan 28 2007 STATUS approved

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Last modified August 15 08:36 EDT 2022. Contains 356130 sequences. (Running on oeis4.)