0,5

Also number of ways to insert two pairs of parentheses into a string of n-4 letters (allowing empty pairs of parentheses). E.g. there are 30 ways for 2 letters. Cf. A002415.

2,10,30,70, ... gives orchard crossing number of complete graph K_n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 28 2003

If Y is a 2-subset of an n-set X then, for n>=4, a(n-1) is the number of 4-subsets and 5-subsets of X having exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007

Middle column of table on Feder and Garber p.6. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 23 2009]

Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 449.

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

M. Aganagic, A. Klemm and C. Vafa, Disk Instantons, Mirror Symmetry and the Duality Web

D. Garber, [math/0303317] The Orchard crossing number of an abstract graph

Elie Feder, David Garber, The Orchard crossing number of an abstract graph, v2, Apr 23, 2009 [From Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 23 2009]

[seq(binomial(n, 4)*2, n=0..40)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 18 2006

seq(sum(sum(sum(k, j=0..k), k=0..m), m=1..n), n=-3..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 26 2008

a:=n->add(binomial(n, 2)+add(binomial(n, 2), j=0..n), j=0..n):seq(a(n)/6, n=-2..30); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]

s1=s2=s3=s4=0; lst={0, 0, 0}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s3], {n, -1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]

A diagonal of A088617.

Cf. A033487, A050534, A060008.

Partial sums of A007290.

Sequence in context: A065137 A034262 A167214 this_sequence A051667 A106355 A120546

Adjacent sequences: A034824 A034825 A034826 this_sequence A034828 A034829 A034830

nonn

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