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A072964 Number of partitions of n-th triangular number n(n+1)/2 (A000217(n)) into triangular parts. 11

%I

%S 1,1,2,4,7,15,32,66,141,295,619,1286,2654,5460,11066,22357,44962,

%T 89258,176459,347103,675846,1309903,2525893,4830943,9196093,17418788,

%U 32772432,61375543,114401182,212026732,391231769,718710706,1313781686

%N Number of partitions of n-th triangular number n(n+1)/2 (A000217(n)) into triangular parts.

%C What is limit_{n->inf} a(n)^(1/n)? [This limit is equal to 1. - _Vaclav Kotesovec_, May 21 2018]

%H T. D. Noe, <a href="/A072964/b072964.txt">Table of n, a(n) for n=0..100</a>

%F 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)).

%F a(n) = A007294(A000217(n)).

%F 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

%t 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_ *)

%Y Cf. A007294, A073420, A114738.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 13 2002

%E Entry revised by _N. J. A. Sloane_, Jan 28 2007

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Last modified May 21 11:54 EDT 2019. Contains 323443 sequences. (Running on oeis4.)