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URL: https://oeis.org/A029609

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A029609
Central numbers in the (2,3)-Pascal triangle A029600.
5
1, 5, 15, 50, 175, 630, 2310, 8580, 32175, 121550, 461890, 1763580, 6760390, 26001500, 100291500, 387793800, 1502700975, 5834015550, 22687838250, 88363159500, 344616322050, 1345644686100, 5260247409300, 20583576819000, 80619009207750, 316026516094380, 1239796332370260
OFFSET
0,2
COMMENTS
For n > 0 also central terms of (1,4)-Pascal triangle A095666. - Reinhard Zumkeller, Apr 08 2012
LINKS
FORMULA
From Peter Bala, Aug 16 2011: (Start)
a(n) = (5/2)*binomial(2*n,n) for n >= 1.
O.g.f.: -3/2 + (5/2) * 1/sqrt(1-4*x) = 1+5*x+15*x^2+50*x^3+... = 1+5*x*d/dx(log(C(x))), where C(x) is the o.g.f. for the Catalan numbers A000108. (End)
E.g.f.: (5*exp(2*x)*BesselI(0, 2*x) - 3)/2. - Stefano Spezia, Feb 14 2025
a(n) ~ 5 * 2^(2*n-1) / sqrt(Pi*n). - Amiram Eldar, Sep 26 2025
MATHEMATICA
a[n_]=(5*Binomial[2*n, n]-3KroneckerDelta[n, 0])/2; Array[a, 27, 0] (* Stefano Spezia, Feb 14 2025 *)
PROG
(Haskell)
a029609 n = a029600 (2*n) n -- Reinhard Zumkeller, Apr 08 2012
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from James Sellers
STATUS
approved