0,3

sum{k=0..floor(n/2), binomial(n-k,k)(-1)^k*A100071(n-2k)}=1.

Hankel transform is (-1)^n*n*2^(n-1), A085750. This is the inverse binomial transform of -n. - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007

Corollary 3 of "An Identity Involving the Least Common Multiple of Binomial Coefficients and its Application" mentions this sequence. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2009]

Bakir Farhi, An Identity Involving the Least Common Multiple of Binomial Coefficients and its Application, American Mathematical Monthly, Nov. 2009, page 838 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2009]

G.f.: 2x(1-sqrt(1-4x^2))/(sqrt(1-4x^2)(sqrt(1-4x^2)+2x-1)^2); G.f.: (1/sqrt(1-4x^2))x*c(x^2)/(1-x*c(x^2))^2; a(n)=sum{k=0..floor(n/2), binomial(n, k)*(n-2k)}.

a(n)=n*C(n-1,floor((n-1)/2)); a(n)=sum(C(n,k)*2^(n-k)*C(2k-2,k-1)(-1)^(k-1),k,0,n); - Paul Barry (pbarry(AT)wit.ie), Jan 11 2007

Starting (1, 2, 6, 12,...), = inverse binomial transform of A134757: (1, 3, 11, 37, 123, 401,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 08 2007

a(n) = a(n-1)*n/floor(n/2) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 20 2008

G.f.: x/((1-2x)*sqrt(1-4x^2)); - Paul Barry (pbarry(AT)wit.ie), Apr 25 2008

a(n) = (floor(n/2) + ceiling(n/2) + 1)!/(floor(n/2)! * ceiling(n/2)!) [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 04 2008]

seq(seq(binomial(2*j, j)*j*i/2, i=1..2), j=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 28 2007

Table[(Floor[n/2] + Ceiling[n/2] + 1)!/(Floor[n/2]!*Ceiling[n/2]!), {n, 1, 40}] [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Nov 04 2008]

Table[If[n == 0, 0, n*Binomial[n - 1, Floor[(n - 1)/2]]], {n, 0, 30}] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 08 2009]

Cf. A134757.

Sequence in context: A058215 A166456 A162214 this_sequence A129912 A161507 A032177

Adjacent sequences: A100068 A100069 A100070 this_sequence A100072 A100073 A100074

easy,nonn,new

Paul Barry (pbarry(AT)wit.ie), Nov 02 2004