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A095668 Sixth column (m=5) of (1,4)-Pascal triangle A095666. 1

%I

%S 4,21,66,161,336,630,1092,1782,2772,4147,6006,8463,11648,15708,20808,

%T 27132,34884,44289,55594,69069,85008,103730,125580,150930,180180,

%U 213759,252126,295771,345216,401016,463760,534072,612612,700077,797202,904761

%N Sixth column (m=5) of (1,4)-Pascal triangle A095666.

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

%H G. C. Greubel, <a href="/A095668/b095668.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: (4-3*x)/(1-x)^6.

%F a(n) = (n+20)*binomial(n+4, 4)/5.

%F a(n) = 4*b(n) - 3*b(n-1), with b(n) = binomial(n+5, 5) = A000389(n+5, 5).

%F E.g.f.: (480 + 2040*x + 1680*x^2 + 440*x^3 + 40*x^4 + x^5)*exp(x)/120. - _G. C. Greubel_, Nov 25 2017

%F a(n) = Sum_{i=0..n+1} A000217(i)*A055999(n+2-i). - _Bruno Berselli_, Mar 05 2018

%p A095668:=n->(n+20)*binomial(n+4, 4)/5: seq(A095668(n), n=0..80); # _Wesley Ivan Hurt_, Nov 25 2017

%t Table[(n + 20)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* _G. C. Greubel_, Nov 25 2017 *)

%o (PARI) for(n=0,30, print1((n+20)*binomial(n+4, 4)/5, ", ")) \\ _G. C. Greubel_, Nov 25 2017

%o (MAGMA) [(n+20)*Binomial(n+4, 4)/5: n in [0..30]]; // _G. C. Greubel_, Nov 25 2017

%Y Cf. A000389, A095666.

%Y Cf. A000217, A055999.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Jun 11 2004

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)