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

0,19

Links

Seiichi Manyama, Rows n = 0..420, flattened

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Identities

Example

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;

Prog

(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)

Crossrefs

Row sums give A003106.

Cf. A008284, A259361, A268187.

Sequence in context: A194515 A163325 A105186 * A238406 A058709 A025842

Adjacent sequences: A328343 A328344 A328345 * A328347 A328348 A328349

Keyword

nonn,tabf,look

Author

Seiichi Manyama, Oct 13 2019

Status

approved