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A134481 Row sums of triangle A134480.

%I A134481 #23 Oct 09 2023 17:18:35
%S A134481 1,5,20,50,100,175,280,420,600,825,1100,1430,1820,2275,2800,3400,4080,
%T A134481 4845,5700,6650,7700,8855,10120,11500,13000,14625,16380,18270,20300,
%U A134481 22475,24800,27280,29920,32725,35700,38850,42180,45695
%N A134481 Row sums of triangle A134480.
%C A134481 Binomial transform of [1, 4, 11, 4, 1, -1, 1, -1, 1, -1, ...]. Also, 1 followed by 5 * A000292, the tetrahedral numbers; i.e., 1, then 5 * (1, 4, 10, 25, 35, ...).
%C A134481 If Y is a 5-subset of an n-set X then, for n>=8, a(n-7) is the number of 4-subsets of X having exactly one element in common with Y. - _Milan Janjic_, Dec 28 2007
%H A134481 Vincenzo Librandi, <a href="/A134481/b134481.txt">Table of n, a(n) for n = 0..1000</a>
%H A134481 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A134481 a(n) = 5*binomial(n+2,3) for n>0. - _Milan Janjic_, Dec 28 2007
%F A134481 G.f.: 1 + 5*x / (1-x)^4. - _R. J. Mathar_, Apr 04 2012
%F A134481 a(n) = Sum_{i=0..n} (n+i)*(1+i) for n > 0. - _Bruno Berselli_, Dec 16 2013
%F A134481 E.g.f.: 1 + 5*exp(x)*x*(6 + 6*x + x^2)/6. - _Stefano Spezia_, Oct 09 2023
%e A134481 a(2) = 20 = sum of row 3 terms of triangle A134480: (9 + 7 + 4).
%e A134481 a(3) = 50 = (1, 3, 3, 1) dot (1, 4, 11, 4) = (1 + 12 + 33 + 4).
%e A134481 a(2) = 20 = 2*1 + 3*2 + 4*3; a(5) = 5*1 + 6*2 + 7*3 + 8*4 + 9*5 + 10*6. - _Bruno Berselli_, Dec 16 2013
%t A134481 CoefficientList[Series[1+5x/(1-x)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 29 2012 *)
%o A134481 (Magma) I:=[1, 5, 20, 50, 100]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 29 2012
%Y A134481 Cf. A134480, A000292.
%K A134481 nonn,easy
%O A134481 0,2
%A A134481 _Gary W. Adamson_, Oct 27 2007