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A342890 Triangle read by rows: T(n,k) = generalized binomial coefficients (n,k)_11 (n >= 0, 0 <= k <= n).

%I A342890 #20 Apr 03 2021 03:11:59
%S A342890 1,1,1,1,12,1,1,78,78,1,1,364,2366,364,1,1,1365,41405,41405,1365,1,1,
%T A342890 4368,496860,2318680,496860,4368,1,1,12376,4504864,78835120,78835120,
%U A342890 4504864,12376,1,1,31824,32821152,1837984512,6892441920,1837984512,32821152,31824,1
%N A342890 Triangle read by rows: T(n,k) = generalized binomial coefficients (n,k)_11 (n >= 0, 0 <= k <= n).
%C A342890 For references, links, programs, etc., see earlier sequences in this series, especially A342889.
%H A342890 Seiichi Manyama, <a href="/A342890/b342890.txt">Rows n = 0..139, flattened</a>
%F A342890 The generalized binomial coefficient (n,k)_m = Product_{j=1..k} binomial(n+m-j,m)/binomial(j+m-1,m).
%e A342890 Triangle begins:
%e A342890   [1],
%e A342890   [1, 1],
%e A342890   [1, 12, 1],
%e A342890   [1, 78, 78, 1],
%e A342890   [1, 364, 2366, 364, 1],
%e A342890   [1, 1365, 41405, 41405, 1365, 1],
%e A342890   [1, 4368, 496860, 2318680, 496860, 4368, 1],
%e A342890   [1, 12376, 4504864, 78835120, 78835120, 4504864, 12376, 1],
%e A342890   [1, 31824, 32821152, 1837984512, 6892441920, 1837984512, 32821152, 31824, 1],
%e A342890 ...
%o A342890 (PARI) f(n, k, m) = prod(j=1, k, binomial(n-j+m, m)/binomial(j-1+m, m));
%o A342890 T(n, k) = f(n, k, 11); \\ _Seiichi Manyama_, Apr 02 2021
%Y A342890 Triangles of generalized binomial coefficients (n,k)_m (or generalized Pascal triangles) for m = 1,...,12: A007318 (Pascal), A001263, A056939, A056940, A056941, A142465, A142467, A142468, A174109, A342889, A342890, A342891.
%K A342890 nonn,tabl
%O A342890 0,5
%A A342890 _N. J. A. Sloane_, Apr 01 2021