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A118443 Row sums of triangle A118441, which is the matrix log of triangle A118435.

%I A118443 #14 Apr 08 2024 09:13:21
%S A118443 1,-2,3,-36,-155,474,1127,-1992,-1719,-4810,-31669,109332,286637,
%T A118443 -596974,-904785,449136,-3218287,16156782,50232979,-121747380,
%U A118443 -233735691,309853258,15768823,1624290984,6853579225,-19712646746,-44873974053,79998871428,90434035261
%N A118443 Row sums of triangle A118441, which is the matrix log of triangle A118435.
%H A118443 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,-12,0,-86,0,-300,0,-625).
%F A118443 G.f.: (1+x)*(1-3*x+18*x^2-78*x^3+45*x^4-175*x^5)/(1+6*x^2+25*x^4)^2.
%F A118443 E.g.f.: cos(2*x)*((1 - x)*cosh(x) + (1 + 3*x)*sinh(x)) - sin(2*x)*((1 + x)*cosh(x) - (1 - 3*x)*sinh(x)). - _Stefano Spezia_, Jul 01 2023
%t A118443 nmax = 30;
%t A118443 h[n_, k_] := Binomial[n, k]*(-1)^(Quotient[n+1, 2] - Quotient[k, 2]+n-k);
%t A118443 H = Table[h[n, k], {n, 0, nmax}, {k, 0, nmax}];
%t A118443 Cn = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, nmax}];
%t A118443 L = MatrixLog[H.Inverse[Cn].H];
%t A118443 Total /@ Rest@L (* _Jean-François Alcover_, Apr 08 2024 *)
%o A118443 (PARI) {a(n)=polcoeff((1+x)*(1-3*x+18*x^2-78*x^3+45*x^4-175*x^5)/(1+6*x^2+25*x^4 +x*O(x^n))^2,n)}
%Y A118443 Cf. A118441 (triangle), A118442 (column 0), A118444 (a(n)/(n+1)); A118435.
%K A118443 sign,easy
%O A118443 0,2
%A A118443 _Paul D. Hanna_, Apr 28 2006