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A118352 Semi-diagonal (one row below central terms) of pendular triangle A118350 and equal to the self-convolution of the central terms (A118351).

%I A118352 #7 Feb 18 2021 14:18:15
%S A118352 1,2,13,96,770,6530,57612,523446,4864795,46032288,441981816,
%T A118352 4295393886,42172388820,417668676206,4167719552099,41861139949200,
%U A118352 422890327921650,4294027462637528,43801007565527184,448625344231794792
%N A118352 Semi-diagonal (one row below central terms) of pendular triangle A118350 and equal to the self-convolution of the central terms (A118351).
%H A118352 G. C. Greubel, <a href="/A118352/b118352.txt">Table of n, a(n) for n = 0..500</a>
%t A118352 T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==n, 0, T[n-1, k] -3*T[n-1, k-1] +3*T[n, k-1] +T[n+1, k-1] ]];
%t A118352 Table[T[n, n-2], {n,2,30}] (* _G. C. Greubel_, Feb 18 2021 *)
%o A118352 (PARI) {a(n)=polcoeff((serreverse(x*(1-3*x+sqrt((1-3*x)*(1-7*x)+x*O(x^n)))/2/(1-3*x))/x)^2,n)}
%o A118352 (Sage)
%o A118352 @CachedFunction
%o A118352 def T(n, k):
%o A118352     if (k<0 or n<k): return 0
%o A118352     elif (k==0): return 1
%o A118352     elif (k==n): return 0
%o A118352     else: return T(n-1, k) - 3*T(n-1, k-1) + 3*T(n, k-1) + T(n+1, k-1)
%o A118352 [T(n,n-2) for n in (2..30)] # _G. C. Greubel_, Feb 18 2021
%Y A118352 Cf. A118350, A118351, A118353, A118354.
%K A118352 nonn
%O A118352 0,2
%A A118352 _Paul D. Hanna_, Apr 26 2006