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A028322
Central elements in the 5-Pascal triangle A028313.
8
1, 5, 12, 38, 130, 462, 1680, 6204, 23166, 87230, 330616, 1259700, 4820452, 18513068, 71318400, 275467320, 1066432950, 4136847390, 16075953960, 62570669700, 243882320220, 951797460900, 3718872587040, 14545727618760
OFFSET
0,2
LINKS
FORMULA
G.f.: (1 + 3*x)/sqrt(1-4*x). - Vladeta Jovovic, Jan 08 2004
a(n) = A000984(n) + 3*A000984(n-1). - R. J. Mathar, Dec 15 2015
a(n) = (n+1)*(7*n-2)*A000108(n)/(2*(2*n-1)). - G. C. Greubel, Jan 05 2024
MATHEMATICA
Table[(n+1)*(7*n-2)*CatalanNumber[n]/(2*(2*n-1)), {n, 0, 40}] (* G. C. Greubel, Jan 05 2024 *)
PROG
(Magma) [(n+1)*(7*n-2)*Catalan(n)/(2*(2*n-1)): n in [0..40]]; // G. C. Greubel, Jan 05 2024
(SageMath) [(7*n-2)*binomial(2*n, n)/(2*(2*n-1)) for n in range(41)] # G. C. Greubel, Jan 05 2024
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from James A. Sellers
STATUS
approved