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

1,2

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

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

Prog

(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), ", "));

Crossrefs

Cf. A291820, A291821, A277297.

Sequence in context: A000531 A296769 A241524 * A099453 A292535 A026763

Adjacent sequences: A291819 A291820 A291821 * A291823 A291824 A291825

Keyword

nonn

Author

Paul D. Hanna, Sep 01 2017

Status

approved