|
%I #5 Nov 06 2021 20:15:58
%S 1,1,-3,-31,453,15641,-973443,-126707471,32192101173,16547934365321,
%T -16912274385623763,-34670312866958030751,141940412456349939507813,
%U 1163060052394732038435530361,-19053251054424307861590927924003,-624375047526738670923288994646642991
%N G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-2*x)).
%F a(0) = 1; a(n) = -a(n-1) - Sum_{k=0..n-1} (-2)^(k+1) * a(k) * a(n-k-1).
%t nmax = 15; A[_] = 0; Do[A[x_] = 1/(1 + x - 2 x A[-2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[(-2)^(k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}]
%Y Cf. A001003, A015097, A348901.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Nov 06 2021
|
