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

0,2

Links

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

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

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 *)

Prog

(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))

Crossrefs

Cf. A002426, A092683, A092686, A092689.

Sequence in context: A106438 A291382 A109999 * A030186 A289592 A292230

Adjacent sequences: A092687 A092688 A092689 * A092691 A092692 A092693

Keyword

nonn

Author

Paul D. Hanna, Mar 04 2004

Status

approved