A328346 - OEIS

A328346

Triangle read by rows: T(n,k) is the coefficient of x^(n - k*(k+1)) in Product_{j=1..k} 1/(1 - x^j) for n >= 0, 0 <= k <= A259361(n).

%I #27 Oct 14 2019 04:29:06

%S 1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,2,0,1,2,0,1,3,0,1,3,0,1,4,1,0,1,

%T 4,1,0,1,5,2,0,1,5,3,0,1,6,4,0,1,6,5,0,1,7,7,0,1,7,8,0,1,8,10,1,0,1,8,

%U 12,1,0,1,9,14,2,0,1,9,16,3,0,1,10,19,5,0,1,10,21,6

%N Triangle read by rows: T(n,k) is the coefficient of x^(n - k*(k+1)) in Product_{j=1..k} 1/(1 - x^j) for n >= 0, 0 <= k <= A259361(n).

%H Seiichi Manyama, <a href="/A328346/b328346.txt">Rows n = 0..420, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanIdentities.html">Rogers-Ramanujan Identities</a>

%e Triangle begins:

%e 1;

%e 0;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 2;

%e 0, 1, 3;

%e 0, 1, 4, 1;

%e 0, 1, 5, 2;

%e 0, 1, 5, 3;

%e 0, 1, 6, 4;

%e 0, 1, 6, 5;

%e 0, 1, 7, 7;

%e 0, 1, 7, 8;

%e 0, 1, 8, 10, 1;

%o (PARI) T(n, k) = polcoef(1/prod(j=1, k, 1-x^j+x*O(x^n)), n-k*(k+1));

%o tabf(nn) = for(n=0, nn, for(k=0, (-1+sqrt(1+4*n))/2, print1(T(n, k), ", ")); print)

%Y Row sums give A003106.

%Y Cf. A008284, A259361, A268187.

%K nonn,tabf,look

%O 0,19

%A _Seiichi Manyama_, Oct 13 2019