login
Triangle read by rows: T(n,k) = (2 * (binomial(n,k)) * (n + 2 * k + 3)!)/((k + 1)! * (k + 2)! * (n + 3)!).
1

%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