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

1, -2, 3, -36, -155, 474, 1127, -1992, -1719, -4810, -31669, 109332, 286637, -596974, -904785, 449136, -3218287, 16156782, 50232979, -121747380, -233735691, 309853258, 15768823, 1624290984, 6853579225, -19712646746, -44873974053, 79998871428, 90434035261

Offset: 0

Author

Paul D. Hanna, Apr 28 2006

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,-12,0,-86,0,-300,0,-625).

Crossrefs

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

Programs

Mathematica

nmax = 30;
h[n_, k_] := Binomial[n, k]*(-1)^(Quotient[n+1, 2] - Quotient[k, 2]+n-k);
H = Table[h[n, k], {n, 0, nmax}, {k, 0, nmax}];
Cn = Table[Binomial[n, k], {n, 0, nmax}, {k, 0, nmax}];
L = MatrixLog[H.Inverse[Cn].H];
Total /@ Rest@L (* Jean-François Alcover, Apr 08 2024 *)

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)}

Formula

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.

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