A104384 Number of partitions of triangular numbers n*(n+1)/2 into (n-2) distinct parts for n>=3.

1, 4, 12, 27, 57, 110, 201, 352, 598, 984, 1586, 2503, 3882, 5928, 8932, 13287, 19551, 28472, 41078, 58754, 83372, 117417, 164230, 228212, 315190, 432817, 591130, 803192, 1086035, 1461680, 1958596, 2613417, 3473190, 4598073, 6064920, 7971480

Offset: 3

Author

Paul D. Hanna, Mar 04 2005

Keywords

• nonn

Comments

In triangle A104382, equals the second diagonal down from the main diagonal.

Also equals a diagonal with slope -3 in the Partition Numbers triangle A008284, found at n = 3+3k, or T(3+3k,k) for k >=1. - Richard R. Forberg, Dec 02 2014

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 3..132

Crossrefs

Cf. A000009, A104382, A008284.

Programs

PARI

{a(n)=if(n<3,0,polcoeff(polcoeff( prod(i=1,n*(n+1)/2,1+y*x^i,1+x*O(x^(n*(n+1)/2))),n*(n+1)/2,x),n-2,y))}

Formula

From Álvar Ibeas, Jul 23 2020: (Start)

Writing p(m) for A000041(m),

a(n) = p(2n-1) - A000070(n) + 1 and

a(n+1) - a(n) = p(2*n+1) - p(2*n-1) - p(n+1) = A027336(2*n+1) - p(n+1).

(End)