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%I #13 Jun 13 2017 21:56:49
%S 1,2,7,22,71,226,717,2262,7107,22246,69413,215986,670441,2076686,
%T 6420403,19816362,61070499,187953174,577742469,1773918642,5441141589,
%U 16674016758,51052484343,156188410098,477487110429,1458741494826
%N Row sums of triangle A092689, which is related to the central trinomial coefficients (A002426).
%H G. C. Greubel, <a href="/A092690/b092690.txt">Table of n, a(n) for n = 0..1000</a>
%F 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
%t 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 *)
%o (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))
%Y Cf. A002426, A092683, A092686, A092689.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 04 2004
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