0,1

In the Frey-Sellers reference this sequence is called {(n+2) over 4}_{3}, n >= 0.

If X is an n-set and Y a fixed (n-4)-subset of X then a(n-5) is equal to the number of 4-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007

D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Milan Janjic, Two Enumerative Functions

a(n)= A062750(n+2, 4)= (n+6)*(n+1)*(n^2+7*n+16)/4!.

G.f.: N(4;1, x)/(1-x)^5 with N(4;1, x)= 4-6*x+4*x^2-x^3, polynomial of second row of A062751.

[seq(binomial(n, 4)-1, n=5..37)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2006

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

(PARI) { for (n=0, 1000, write("b063258.txt", n, " ", binomial(n + 5, 4) - 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 19 2009]

Fifth column (r=4) of FS(4) staircase array A062750.

A column of triangle A014473.

Cf. A000096, A062748.

Sequence in context: A098942 A011554 A099586 this_sequence A011852 A061989 A079908

Adjacent sequences: A063255 A063256 A063257 this_sequence A063259 A063260 A063261

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001

Simpler definition from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 21 2003

More terms from Milan R. Janjic (agnus(AT)blic.net), Aug 15 2007

More terms from Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 19 2009