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Principal diagonal of the convolution array A213505.
3

%I #20 Oct 31 2023 11:20:50

%S 1,25,170,674,1979,4795,10164,19524,34773,58333,93214,143078,212303,

%T 306047,430312,592008,799017,1060257,1385746,1786666,2275427,2865731,

%U 3572636,4412620,5403645,6565221,7918470,9486190,11292919,13364999,15730640,18419984,21465169

%N Principal diagonal of the convolution array A213505.

%H Clark Kimberling, <a href="/A213546/b213546.txt">Table of n, a(n) for n = 1..200</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 a(n) = (16*n^5 + 15*n^4 - n)/30.

%F a(n) = 6*a(n-1) - 10*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

%F G.f.: x*(1 + 19*x + 35*x^2 + 9*x^3)/(1 - x)^6.

%F E.g.f.: exp(x)*x*(30 + 345*x + 490*x^2 + 175*x^3 + 16*x^4)/30. - _Stefano Spezia_, Oct 28 2023

%t (See A213505.)

%Y Cf. A213505, A213500.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jun 16 2012