A092690 Row sums of triangle A092689, which is related to the central trinomial coefficients (A002426).

1, 2, 7, 22, 71, 226, 717, 2262, 7107, 22246, 69413, 215986, 670441, 2076686, 6420403, 19816362, 61070499, 187953174, 577742469, 1773918642, 5441141589, 16674016758, 51052484343, 156188410098, 477487110429, 1458741494826

Offset: 0

Author

Paul D. Hanna, Mar 04 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002426, A092683, A092686, A092689.

Programs

Mathematica

With[{nn = 50}, CoefficientList[Series[Exp[x]*((1 + x)*BesselI[0, 2*x] + x*BesselI[1, 2*x]), {x,0,nn}], x] Range[0, nn]!] (* G. C. Greubel, Feb 27 2017 *)

PARI

{T(n,k)=if(n<0 || k>n,0, if(n==0 && k==0,1, if(n==1 && k<=1,1, if(k==n-1,T(n-1,0), if(k==n,T(n,0), 2*T(n-1,k)+T(n-1,k+1))))))} a(n)=sum(k=0,n,T(n,k))

Formula

E.g.f.: a(n) = n!* [x^n] exp(x)*((1+x)*BesselI(0, 2*x)+x*BesselI(1, 2*x)). - Peter Luschny, Aug 25 2012