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%I #25 Dec 16 2017 23:26:40
%S 1,11,42,106,215,381,616,932,1341,1855,2486,3246,4147,5201,6420,7816,
%T 9401,11187,13186,15410,17871,20581,23552,26796,30325,34151,38286,
%U 42742,47531,52665,58156,64016,70257,76891
%N Principal diagonal of the convolution array A213771.
%H Clark Kimberling, <a href="/A213772/b213772.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: x*(1 + 7*x + 4*x^2)/(1 - x)^4.
%F a(n) = (4*n^2-3*n+1)*n/2 = n*A002411(n) - (n-1)*A002411(n-1). [_Bruno Berselli_, Dec 11 2012]
%F a(n) = n*A000326(n) + sum( A000326(i), i=0..n-1 ). [_Bruno Berselli_, Dec 18 2013]
%t (See A213771.)
%o (PARI) a(n) = (4*n^3-3*n^2+n)/2; \\ _Altug Alkan_, Dec 16 2017
%Y Cf. A000326, A002411, A213771, A220084 (for a list of numbers of the form n*P(k,n)-(n-1)*P(k,n-1), where P(k,n) is the n-th k-gonal pyramidal number).
%Y Cf. A260260 (comment). [_Bruno Berselli_, Jul 22 2015]
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 04 2012
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