A118443 - OEIS

%I #14 Apr 08 2024 09:13:21

%S 1,-2,3,-36,-155,474,1127,-1992,-1719,-4810,-31669,109332,286637,

%T -596974,-904785,449136,-3218287,16156782,50232979,-121747380,

%U -233735691,309853258,15768823,1624290984,6853579225,-19712646746,-44873974053,79998871428,90434035261

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

%H <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 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 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 nmax = 30;

%t h[n_, k_] := Binomial[n, k]*(-1)^(Quotient[n+1, 2] - Quotient[k, 2]+n-k);

%t H = Table[h[n, k], {n, 0, nmax}, {k, 0, nmax}];

%t Cn = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, nmax}];

%t L = MatrixLog[H.Inverse[Cn].H];

%t Total /@ Rest@L (* _Jean-François Alcover_, Apr 08 2024 *)

%o (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 Cf. A118441 (triangle), A118442 (column 0), A118444 (a(n)/(n+1)); A118435.

%K sign,easy

%O 0,2

%A _Paul D. Hanna_, Apr 28 2006