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%I #16 Jun 23 2024 10:35:17
%S 1,2,11,52,200,742,2752,10278,38670,146426,557408,2131318,8179646,
%T 31491202,121568150,470404274,1823968074,7085220834,27567196704,
%U 107414120214,419080195374,1636990646274,6401210885934,25055584929954,98160790785714,384885441746202,1510279309724502
%N Self-convolution of array T given by A026615.
%H G. C. Greubel, <a href="/A026956/b026956.txt">Table of n, a(n) for n = 0..1000</a>
%F From _G. C. Greubel_, Jun 17 2024: (Start)
%F a(n) = Sum_{k=0..n} A026615(n, k) * A026615(n, n-k).
%F a(n) = A000108(n-2)*(49*n^2 - 105*n + 48)/n - 6, for n >= 1, with a(0) = 1.
%F G.f.: (4 - 8*x + 5*x^2 - x^3 - (3 - x + 4*x^2)*sqrt(1-4*x))/((1-x)*sqrt(1-4*x)).
%F E.g.f.: (1/6)*( 18 + 24*x - 36*exp(x) + 4*exp(2*x)*(6 - 6*x + x^2) * BesselI(0, 2*x) + x*exp(2*x)*(23 - 4*x)*BesselI(1, 2*x) ). (End)
%t Table[If[n==0, 1, CatalanNumber[n-2]*(49*n^2-105*n+48)/n -6], {n,0,40}] (* _G. C. Greubel_, Jun 17 2024 *)
%o (Magma) [n le 1 select n+1 else Catalan(n-2)*(49*n^2-105*n+48)/n - 6: n in [0..40]]; // _G. C. Greubel_, Jun 17 2024
%o (SageMath) [1,2]+[catalan_number(n-2)*(49*n^2-105*n+48)/n -6 for n in range(2,41)] # _G. C. Greubel_, Jun 17 2024
%Y Cf. A000108, A026615, A026616, A026617, A026618, A026619, A026620.
%Y Cf. A026621, A026622, A026623, A026624, A026625, A026957, A026958.
%Y Cf. A026959, A026960.
%K nonn
%O 0,2
%A _Clark Kimberling_
%E More terms from _Sean A. Irvine_, Oct 20 2019
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