A096942 - OEIS

%I #23 Aug 29 2024 06:04:25

%S 5,21,55,115,210,350,546,810,1155,1595,2145,2821,3640,4620,5780,7140,

%T 8721,10545,12635,15015,17710,20746,24150,27950,32175,36855,42021,

%U 47705,53940,60760,68200,76296,85085,94605,104895,115995,127946,140790,154570,169330,185115

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

%C 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

%H Vincenzo Librandi, <a href="/A096942/b096942.txt">Table of n, a(n) for n = 0..1000</a>

%F 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).

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

%F a(n) = Sum_{k=1..n} (Sum_{i=1..k} i*(n-k+5)). - _Wesley Ivan Hurt_, Sep 26 2013

%t Table[(n + 20) Binomial[n + 3, 3]/4, {n, 0, 100}]

%t CoefficientList[Series[(5 - 4 x)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 01 2013 *)

%o (Magma) [(n + 20)*Binomial(n + 3, 3) div 4: n in [0..50]]; // _Vincenzo Librandi_, Oct 01 2013

%Y Fourth column: A096941; sixth column: A096943.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Jul 16 2004