A029609 Central numbers in the (2,3)-Pascal triangle A029600.

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

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

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

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

Cf. A000108, A029600, A095666.

Sequence in context: A344204 A034539 A340395 * A014274 A363510 A120825

Adjacent sequences: A029606 A029607 A029608 * A029610 A029611 A029612

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved