A096942 Fifth column of (1,5)-Pascal triangle A096940.

5, 21, 55, 115, 210, 350, 546, 810, 1155, 1595, 2145, 2821, 3640, 4620, 5780, 7140, 8721, 10545, 12635, 15015, 17710, 20746, 24150, 27950, 32175, 36855, 42021, 47705, 53940, 60760, 68200, 76296, 85085, 94605, 104895, 115995, 127946, 140790, 154570, 169330, 185115

Offset: 0

Author

Wolfdieter Lang, Jul 16 2004

Keywords

• nonn
• easy

Comments

If Y is a 5-subset of an n-set X then, for n>=8, a(n-8) is the number of 4-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Fourth column: A096941; sixth column: A096943.

Programs

Magma

[(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // Vincenzo Librandi, Oct 01 2013

Mathematica

Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]
CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 01 2013 *)

Formula

a(n) = (n+20)*binomial(n+3, 3)/4 = 5*b(n) - 4*b(n-1), with b(n) = A000332(n+4) = binomial(n+4, 4).

G.f.: (5-4*x)/(1-x)^5.

a(n) = Sum_{k=1..n} (Sum_{i=1..k} i*(n-k+5)). - Wesley Ivan Hurt, Sep 26 2013