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A092371 Triangle read by rows: T(n, k) = binomial(n, k) * binomial(n+k, n-k).

%I A092371 #17 Jan 04 2025 12:00:46
%S A092371 1,6,1,18,15,1,40,90,28,1,75,350,280,45,1,126,1050,1680,675,66,1,196,
%T A092371 2646,7350,5775,1386,91,1,288,5880,25872,34650,16016,2548,120,1,405,
%U A092371 11880,77616,162162,126126,38220,4320,153,1,550,22275,205920,630630
%N A092371 Triangle read by rows: T(n, k) = binomial(n, k) * binomial(n+k, n-k).
%C A092371 Related to the coefficients of x^k y^k in the n-th power of x^2 + x*y + 2*x + y + 1. - _F. Chapoton_, Jan 04 2025
%F A092371 T(n, k) = [x^(n-k)] F(-n, -n-k; 1; x). - _Paul Barry_, Sep 04 2008
%e A092371 Triangle starts:
%e A092371   [1]   1;
%e A092371   [2]   6,    1;
%e A092371   [3]  18,   15,     1;
%e A092371   [4]  40,   90,    28,     1;
%e A092371   [5]  75,  350,   280,    45,     1;
%e A092371   [6] 126, 1050,  1680,   675,    66,    1;
%e A092371   [7] 196, 2646,  7350,  5775,  1386,   91,   1;
%e A092371   [8] 288, 5880, 25872, 34650, 16016, 2548, 120, 1;
%p A092371 T := (n, k) -> binomial(n, k) * binomial(n+k, n-k):  # _Peter Luschny_, Jan 04 2025
%o A092371 (PARI) T(n,k) = binomial(n,k)*binomial(n+k,n-k)
%Y A092371 First column = A002411, second column = A001297, third column = A107418, fourth column = A105251, fifth column = A104673.
%Y A092371 Main diagonal = 1, second diagonal = A000384.
%Y A092371 Cf. A063007, A006480 (central terms), A082759 (row sums + 1).
%Y A092371 Cf. A104684.
%K A092371 nonn,tabl
%O A092371 1,2
%A A092371 _Benoit Cloitre_, Mar 20 2004