%I A027914
%S A027914 1,2,6,17,50,147,435,1290,3834,11411,34001,101400,302615,903632,
%T A027914 2699598,8068257,24121674,72137547,215786649,645629160,1932081885,
%U A027914 5782851966,17311097568,51828203475,155188936431,464732722872
%N A027914 T(n,0) + T(n,1) + ... + T(n,n), T given by A027907.
%C A027914 Let b(n)=a(n) mod 2; then b(n)=1/2+(-1)^n*(1/2-A010060(floor(n/2))) - 
               Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 23 2004
%C A027914 Binomial transform of A027306 . Inverse binomial transform of = A032443 
               . Hankel transform is {1, 2, 3, 4, ..., n, ...} . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jul 20 2005
%C A027914 Sums of rows of the triangle in A111808. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 17 2005
%F A027914 a(n) = ( 3^n + A002426(n) )/2; lim n -> infinity a(n+1)/a(n) = 3; 3^n 
               < 2*a(n) < 3^(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 
               28 2002
%F A027914 a(n)= (1/2) *(sum(k=0, n, binomial(n, k)*binomial(n-k, k))+3^n); a(n)=sum(k=0, 
               n, sum(i=0, k, binomial(n, i)*binomial(n-i, k))); a(n)=3^n/2*(1+c/
               sqrt(n)+0(n^-1/2)) where c=0.5... - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 26 2003
%F A027914 a(n)=n!*sum(i+j+k=n, 1/(i!*j!*k!)) 0<=i<=n, 0<=k<=j<=n - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Mar 23 2004
%F A027914 G.f.: (1+x+sqrt(1-2x-3x^2))/(2(1-2x-3x^2)); a(n)=sum{k=0..n, floor((k+2)/
               2)*sum{i=0..floor((n-k)/2), C(n, i)C(n-i, i+k)((k+1)/(i+k+1))}}; 
               - Paul Barry (pbarry(AT)wit.ie), Sep 23 2005; corrected Jan 20 2008
%o A027914 (PARI) a(n)=sum(i=0,n,polcoeff((1+x+x^2)^n,i,x))
%o A027914 (PARI) a(n)=sum(i=0,n,sum(j=0,n,sum(k=0,j,if(i+j+k-n,0,(n!/i!/j!/k!)))))
%Y A027914 Cf. A025191, A027915, A081673.
%Y A027914 Cf. A092255.
%Y A027914 Sequence in context: A026165 A148445 A148446 this_sequence A098703 A025272 
               A148447
%Y A027914 Adjacent sequences: A027911 A027912 A027913 this_sequence A027915 A027916 
               A027917
%K A027914 nonn
%O A027914 0,2
%A A027914 Clark Kimberling (ck6(AT)evansville.edu)