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).
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, 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, 12, 1, 0, 1, 9, 14, 2, 0, 1, 9, 16, 3, 0, 1, 10, 19, 5, 0, 1, 10, 21, 6
Offset: 0
Examples
Triangle begins: 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, 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;
Links
- Seiichi Manyama, Rows n = 0..420, flattened
- Eric Weisstein's World of Mathematics, Rogers-Ramanujan Identities
Programs
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PARI
T(n, k) = polcoef(1/prod(j=1, k, 1-x^j+x*O(x^n)), n-k*(k+1)); tabf(nn) = for(n=0, nn, for(k=0, (-1+sqrt(1+4*n))/2, print1(T(n, k), ", ")); print)