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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
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
Sequence in context: A308526 A162678 A265867 * A177456 A360238 A216029
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.)