0,2

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

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

Sums of rows of the triangle in A111808. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2005

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

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

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

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

(PARI) a(n)=sum(i=0, n, polcoeff((1+x+x^2)^n, i, x))

(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!)))))

Cf. A025191, A027915, A081673.

Cf. A092255.

Sequence in context: A026165 A148445 A148446 this_sequence A098703 A025272 A148447

Adjacent sequences: A027911 A027912 A027913 this_sequence A027915 A027916 A027917

nonn

Clark Kimberling (ck6(AT)evansville.edu)