A213549 - OEIS

%I #20 Nov 20 2022 13:52:19

%S 1,12,53,155,360,721,1302,2178,3435,5170,7491,10517,14378,19215,25180,

%T 32436,41157,51528,63745,78015,94556,113597,135378,160150,188175,

%U 219726,255087,294553,338430,387035,440696,499752,564553,635460

%N Principal diagonal of the convolution array A213548.

%H Clark Kimberling, <a href="/A213549/b213549.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: x*(1 + 7*x  + 3*x^2)/(1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

%F a(n) = (11*n^4 + 14*n^3 + n^2 - 2*n)/24 = n*(n+1)*(11*n^2 + 3*n - 2)/24.

%F a(n) = Sum_{i=1..n} (n-i+1)*A000217(n+i-1), see A213548. - _Bruno Berselli_, Oct 05 2016

%t (See A213548.)

%t LinearRecurrence[{5,-10,10,-5,1},{1,12,53,155,360},40] (* _Harvey P. Dale_, Nov 20 2022 *)

%Y Cf. A000217, A213500, A213548.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 16 2012