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%I #15 Aug 20 2021 06:36:12
%S 1,1,1,2,6,16,46,176,722,2906,13106,66716,345676,1849992,10802156,
%T 66543296,418075036,2750329276,19145683612,137410493656,1012831509736,
%U 7785886770656,62105849642376,507682088621632,4271236045340056,37171085370443576
%N E.g.f. exp(x+1/6*x^3+1/24*x^4)
%F a(n)=n!*sum(k=0..n, sum(j=floor((n-k)/3)..floor((n-k)/2), binomial(j,n-k-2*j)*binomial(k,j)*2^(-2*n+2*k+3*j)*3^(-j))/k!).
%F D-finite with recurrence +6*a(n) -6*a(n-1) -3*(n-1)*(n-2)*a(n-3) -(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 20 2021
%t With[{nn=30},CoefficientList[Series[Exp[x+x^3/6+x^4/24],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Apr 08 2018 *)
%o (Maxima)
%o a(n):=n!*sum(sum(binomial(j,n-k-2*j)*binomial(k,j)*2^(-2*n+2*k+3*j)*3^(-j),j,floor((n-k)/3),floor((n-k)/2))/k!,k,0,n);
%K nonn
%O 0,4
%A _Vladimir Kruchinin_, May 26 2011
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