%I #16 Nov 09 2019 10:43:03
%S 1,1,5,1,14,42,1,28,210,462,1,48,660,3432,6006,1,75,1650,15015,60060,
%T 87516,1,110,3575,50050,340340,1108536,1385670,1,154,7007,140140,
%U 1429428,7759752,21339318,23371634,1,208,12740,346528,4938024,39504192,178474296,424938800,414315330
%N Triangle read by rows: T(n,k) = (2 * (binomial(n,k)) * (n + 2 * k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!).
%e Triangle begins:
%e 1;
%e 1, 5;
%e 1, 14, 42;
%e 1, 28, 210, 462;
%e ...
%o (PARI) t(n, k) = (2 * (binomial(n,k)) * (n + 2*k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!) \\ _Michel Marcus_, Jun 26 2013
%Y Row sums give A087659. Right diagonal gives A005789.
%K nonn,tabl,easy
%O 0,3
%A _Bill Gosper_, Sep 30 2003
%E More terms from _Ray Chandler_, Sep 30 2003