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 A259550 a(n) = C(5*n-1,2*n)/3, n > 0, a(0) = 1. 1
 1, 2, 42, 1001, 25194, 653752, 17298645, 463991880, 12570420330, 343176898988, 9425842448792, 260170725132045, 7210477496434485, 200519284375732896, 5592628786362932776, 156375886125188595376, 4382048530314336892010, 123033460966787345446836 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..17. D. Kruchinin and V. Kruchinin, A Method for Obtaining Generating Function for Central Coefficients of Triangles, Journal of Integer Sequence, Vol. 15 (2012), article 12.9.3. V. V. Kruchinin and D. V. Kruchinin, Composita and its properties, J. Analysis and Number Theory 2 (2014), 1-8. V. V. Kruchinin and D. V. Kruchinin, A Generating Function for the Diagonal T_{2n,n} in Triangles, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.6. D. V. Kruchinin, On solving some functional equations, Advances in Difference Equations, Vol. 1 (2015), 1687-1847. FORMULA G.f.: A(x) = 1 + (x*B(x)')/(B(x)), B(x) = (1 + x*B(x)^5)*(C(x*B(x)^5), C(x) is g.f. of Catalan numbers. a(n) = n*Sum_{i = 0..n}((C(5*n,i)*C(7*n-2*i-1,n-i))/(6*n-i)), n > 1, a(0) = 1. a(n) = 1/5*A001450(n) for n >= 1. exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 2*x + 23*x^2 + 377*x^3 + ... is the o.g.f. for the sequence of Duchon numbers A060941. - Peter Bala, Oct 05 2015 MATHEMATICA Join[{1}, Table[Binomial[5 n - 1, 2 n]/3, {n, 30}]] (* Vincenzo Librandi, Jul 01 2015 *) PROG (Maxima) makelist(if n=0 then 1 else binomial(5*n-1, 2*n)/3, n, 0, 20); (PARI) vector(20, n, n--; if (n==0, 1, binomial(5*n-1, 2*n)/3)) \\ Michel Marcus, Jul 01 2015 (Magma) [1] cat [Binomial(5*n-1, 2*n)/3: n in [1..20]]; // Vincenzo Librandi, Jul 01 2015 CROSSREFS Cf. A000108, A167422, A001450, A060941. Sequence in context: A308526 A162678 A265867 * A177456 A360238 A216029 Adjacent sequences: A259547 A259548 A259549 * A259551 A259552 A259553 KEYWORD nonn,easy AUTHOR Vladimir Kruchinin, Jun 30 2015 EXTENSIONS More terms from Vincenzo Librandi, Jul 01 2015 STATUS approved

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Last modified April 14 09:06 EDT 2024. Contains 371657 sequences. (Running on oeis4.)