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 A319578 a(n) = (1/3)*(n+2)^2*(3*n+3)!/(n+2)!^3. 0
 1, 10, 140, 2310, 42042, 816816, 16628040, 350574510, 7595781050, 168212023980, 3792416540640, 86787993910800, 2011383287449200, 47123837020238400, 1114478745528638160, 26575401262863040830, 638330716607984804250, 15431925043610580004500, 375239440534109892741000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of Schröder paths of length 2n+1 having n peaks. LINKS FORMULA a(n) = (n+2)*(3*n+2)!/((n+2)!^2*n!). a(n) = A060693(2n+1,n). MAPLE a := n -> (n+2)*(3*n+2)!/((n+2)!^2*n!): seq(a(n), n = 0..18); MATHEMATICA Table[(n+2) (3*n+2)! / ((n+2)!^2 n!), {n, 0, 30}] (* Vincenzo Librandi, Oct 01 2018 *) PROG (PARI) a(n) = (1/3)*(n+2)^2*(3*n+3)!/(n+2)!^3; \\ Michel Marcus, Oct 01 2018 (MAGMA) [(1/3)*(n+2)^2*Factorial(3*n+3)/Factorial(n+2)^3: n in [0..20]]; // Vincenzo Librandi, Oct 01 2018 CROSSREFS Cf. A007004, A060693, A215287. Sequence in context: A132505 A254336 A215289 * A051618 A295034 A221576 Adjacent sequences:  A319575 A319576 A319577 * A319579 A319580 A319581 KEYWORD nonn AUTHOR Peter Luschny, Sep 30 2018 STATUS approved

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)