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 A291822 A diagonal of triangle A291820. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 10 22:38 EST 2023. Contains 367717 sequences. (Running on oeis4.)