0,2

The sequence 0,1,8,... has a(n)=n^2*2^(n-1) and is the binomial transform of the hexagonal numbers A000384 (with leading 0). - Paul Barry (pbarry(AT)wit.ie), Jun 09 2003

As 0,1,8,... this is n^2*2^(n-1), the binomial transform of the hexagonal numbers A000384 (include the leading 0). Partial sums are A036826. - Paul Barry (pbarry(AT)wit.ie), Jun 10 2003

Sequence gives total value of all possible sums of distinct odd integers with maximum term less than 2n+1. e.g. for a(3) we can have 1,3,5,1+3,1+5,3+5,1+3+5 = 1+3+5+4+6+8+9 = 36 - Jon Perry (perry(AT)globalnet.co.uk), Feb 06 2004

a(n) = (n+1)^2*2^n = A007758(n+1)/2. - Henry Bottomley (se16(AT)btinternet.com), Jun 13 2001

The binomial transform of 0, 1, 8, ... is A077616. - Paul Barry (pbarry(AT)wit.ie), Jul 24 2003

a(1)=1, a(n)=2a(n-1)+(2n-1)*2^(n-1) - Jon Perry (perry(AT)globalnet.co.uk), Feb 06 2004

a(n) = sum of (n+1)-th row of the triangle in A118416. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 27 2006

Sum(binomial(n,j)*n*j,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 19 2006

a:=n->sum(binomial(n, j)*n*j, j=0..n): seq(a(n), n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 19 2006

a:=n->sum(n*numbcomb(n)/2, j=1..n): seq(a(n), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

f[n_]:=(n^2*2^n)/2; Table[f[n], {n, 0, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 05 2009]

Cf. A118414.

Sequence in context: A131123 A055910 A022573 this_sequence A034998 A121255 A024208

Adjacent sequences: A014474 A014475 A014476 this_sequence A014478 A014479 A014480

nonn

N. J. A. Sloane (njas(AT)research.att.com).