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 A344500 a(n) = Sum_{k=0..n} binomial(n, k)*CT(n, k) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*CT(n, k), where CT(n, k) is the Catalan triangle A053121. 1
 1, 1, 2, 7, 21, 66, 216, 715, 2395, 8101, 27598, 94568, 325612, 1125632, 3904512, 13583195, 47373255, 165585883, 579907758, 2034443127, 7148313381, 25151582046, 88607951512, 312518438532, 1103393962996, 3899415207676, 13792683831176, 48825746365672, 172971084083752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = Sum_{j=0..n} even(n + j)*binomial(n, j)*binomial(n + 1, (n - j)/2)*(j + 1)/(n + 1), where even(k) = 1 if k is even and otherwise 0. MAPLE a := n -> add((if n + j mod 2 = 1 then 0 else binomial(n, j)*binomial(n + 1, (n - j)/2)*(j + 1)/(n + 1) fi), j = 0..n): seq(a(n), n = 0..28); CROSSREFS Cf. A053121, A344501. Sequence in context: A331722 A052911 A126133 * A186240 A274203 A330058 Adjacent sequences:  A344497 A344498 A344499 * A344501 A344502 A344503 KEYWORD nonn AUTHOR Peter Luschny, May 22 2021 STATUS approved

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Last modified November 28 08:12 EST 2021. Contains 349401 sequences. (Running on oeis4.)