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A118437 Row sums of triangle A118435.

%I A118437 #8 Oct 18 2024 08:23:02
%S A118437 1,2,0,8,-32,-128,320,128,2048,8192,-15360,2048,-131072,-524288,
%T A118437 1064960,32768,8388608,33554432,-66846720,524288,-536870912,
%U A118437 -2147483648,4299161600,8388608,34359738368,137438953472,-274810798080,134217728
%N A118437 Row sums of triangle A118435.
%H A118437 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2, -4, 8, -64, 128, -256, 512).
%F A118437 G.f.: (1+8*x^3-32*x^5+384*x^6-256*x^7)/(1-2*x)/(1+4*x^2)/(1+64*x^4).
%t A118437 nmax = 27;
%t A118437 h[n_, k_] := Binomial[n, k]*(-1)^(Quotient[n+1, 2] - Quotient[k, 2]+n-k);
%t A118437 H = Table[h[n, k], {n, 0, nmax}, {k, 0, nmax}];
%t A118437 Cn = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, nmax}];
%t A118437 Total /@ (H.Inverse[Cn].H ) (* _Jean-François Alcover_, Apr 08 2024 *)
%o A118437 (PARI) {a(n)=polcoeff((1+8*x^3-32*x^5+384*x^6-256*x^7)/(1-2*x)/(1+4*x^2)/(1+64*x^4+x*O(x^n)),n)}
%Y A118437 Cf. A118435 (triangle), A118436 (column 0).
%K A118437 sign
%O A118437 0,2
%A A118437 _Paul D. Hanna_, Apr 28 2006