A291822 A diagonal of triangle A291820.

1, 7, 38, 189, 904, 4242, 19723, 91366, 423124, 1963169, 9138416, 42718416, 200656644, 947423923, 4497458118, 21465533955, 103001236168, 496832195860, 2408570061810, 11732479621260, 57410235742920, 282124153996425, 1391949415580256, 6893204658852960, 34254642268407820, 170769192927927532, 853864581906454264, 4281167768111675732, 21519922572920909984

Offset: 1

Author

Paul D. Hanna, Sep 01 2017

Keywords

• nonn

Comments

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

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..70

Crossrefs

Cf. A291820, A291821, A277297.

Programs

PARI

/* As a diagonal of triangle A291820 */
{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)}
for(n=1, 20, print1(A291820(n+2, n-1), ", "));

Formula

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

a(n) = A277297(n) / 2 for n >= 1. - Paul D. Hanna, Jul 24 2023