0,7

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. f. Math., 73 (1969), 7-30.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

G.f.: x^5/((1-2*x)*(1-x)^5).

a(n)=sum{k=0..n, C(n, k+5)} = sum{k=5..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 4). - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004

a:=n->sum(binomial(n, 2*j), j=3..n): seq(a(n), n=1..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 12 2007

A002664:=1/(2*z-1)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]

a=1; lst={}; s1=s2=s3=s4=s5=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; AppendTo[lst, s5]; a=a*2, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 10 2009]

Table[Sum[ Binomial[n + 5, k + 5], {k, 0, n}], {n, -5, 25}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]

a(n) = A055248(n, 5). Partial sums of A002663.

Cf. A000079, A000225, A000295, A002662, A002663, A035038-A035042.

Sequence in context: A001779 A053295 A055798 this_sequence A042609 A002941 A102485

Adjacent sequences: A002661 A002662 A002663 this_sequence A002665 A002666 A002667

nonn,easy

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