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A092690 Row sums of triangle A092689, which is related to the central trinomial coefficients (A002426). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 26 10:57 EDT 2019. Contains 321491 sequences. (Running on oeis4.)