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

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]

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: A129682 A129981 A358824 * A247291 A030033 A364596

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