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URL: https://oeis.org/A055796

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A055796
T(2n+3,n), array T as in A055794.
6
1, 5, 16, 42, 98, 210, 420, 792, 1419, 2431, 4004, 6370, 9828, 14756, 21624, 31008, 43605, 60249, 81928, 109802, 145222, 189750, 245180, 313560, 397215, 498771, 621180, 767746, 942152, 1148488, 1391280, 1675520, 2006697, 2390829, 2834496, 3344874, 3929770
OFFSET
0,2
COMMENTS
If Y is a 2-subset of an n-set X then, for n>=6, a(n-6) is the number of 6-subsets of X which do not have exactly one element in common with Y. - Milan Janjic, Dec 28 2007
LINKS
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7.
FORMULA
a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+30)/720.
a(n-4) = binomial(n,6) + binomial(n,4) for n>3. - Zerinvary Lajos, Jul 24 2006
G.f.: (1-2*x+2*x^2)/(1-x)^7. - Colin Barker, Feb 22 2012
MAPLE
seq(binomial(n+4, 6)+binomial(n+4, 4), n=0..33) # Zerinvary Lajos, Jul 24 2006
MATHEMATICA
a=1; b=2; c=3; d=4; s=5; lst={1, s}; Do[a+=n; b+=a; c+=b; d+=c; s+=d; AppendTo[lst, s], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 5, 16, 42, 98, 210, 420}, 50] (* Vincenzo Librandi, Apr 30 2012 *)
Table[(n+1)(n+2)(n+3)(n+4)(n^2-n+30)/720, {n, 0, 50}] (* Harvey P. Dale, Feb 12 2013 *)
PROG
(Magma) [(n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+30)/720: n in [0..40]]; // Vincenzo Librandi, Apr 30 2012
CROSSREFS
Sequence in context: A097810 A187004 A255135 * A002662 A143962 A321959
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 28 2000
EXTENSIONS
More terms from Harvey P. Dale, Feb 12 2013
STATUS
approved