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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 A328346 #28 Feb 16 2025 08:33:58
%S A328346 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 A328346 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 A328346 12,1,0,1,9,14,2,0,1,9,16,3,0,1,10,19,5,0,1,10,21,6
%N 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).
%H A328346 Seiichi Manyama, <a href="/A328346/b328346.txt">Rows n = 0..420, flattened</a>
%H A328346 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rogers-RamanujanIdentities.html">Rogers-Ramanujan Identities</a>
%e A328346 Triangle begins:
%e A328346   1;
%e A328346   0;
%e A328346   0, 1;
%e A328346   0, 1;
%e A328346   0, 1;
%e A328346   0, 1;
%e A328346   0, 1, 1;
%e A328346   0, 1, 1;
%e A328346   0, 1, 2;
%e A328346   0, 1, 2;
%e A328346   0, 1, 3;
%e A328346   0, 1, 3;
%e A328346   0, 1, 4,  1;
%e A328346   0, 1, 4,  1;
%e A328346   0, 1, 5,  2;
%e A328346   0, 1, 5,  3;
%e A328346   0, 1, 6,  4;
%e A328346   0, 1, 6,  5;
%e A328346   0, 1, 7,  7;
%e A328346   0, 1, 7,  8;
%e A328346   0, 1, 8, 10, 1;
%o A328346 (PARI) T(n, k) = polcoef(1/prod(j=1, k, 1-x^j+x*O(x^n)), n-k*(k+1));
%o A328346 tabf(nn) = for(n=0, nn, for(k=0, (-1+sqrt(1+4*n))/2, print1(T(n, k), ", ")); print)
%Y A328346 Row sums give A003106.
%Y A328346 Cf. A008284, A259361, A268187.
%K A328346 nonn,tabf,look
%O A328346 0,19
%A A328346 _Seiichi Manyama_, Oct 13 2019