A291822 - OEIS

%I #8 Jul 24 2023 18:41:21

%S 1,7,38,189,904,4242,19723,91366,423124,1963169,9138416,42718416,

%T 200656644,947423923,4497458118,21465533955,103001236168,496832195860,

%U 2408570061810,11732479621260,57410235742920,282124153996425,1391949415580256,6893204658852960,34254642268407820,170769192927927532,853864581906454264,4281167768111675732,21519922572920909984

%N A diagonal of triangle A291820.

%C An adjacent diagonal of triangle A291820 equals the Catalan numbers (A000108).

%H Paul D. Hanna, <a href="/A291822/b291822.txt">Table of n, a(n) for n = 1..70</a>

%F a(n) = A291820(n+2, n-1) for n >= 1.

%F a(n) = A277297(n) / 2 for n >= 1. - _Paul D. Hanna_, Jul 24 2023

%o (PARI) /* As a diagonal of triangle A291820 */

%o {A291820(n, k) = my(A=x); for(i=1, n, A = x + subst(x*A, x, y*A + (1-y)*x +x*O(x^n)) ); polcoeff(polcoeff(A, n, x), k, y)}

%o for(n=1, 20, print1(A291820(n+2, n-1), ", "));

%Y Cf. A291820, A291821, A277297.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 01 2017