|
|
A351938
|
|
a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).
|
|
0
|
|
|
1, 1, 1, 3, 5, 9, 17, 35, 65, 125, 241, 463, 885, 1701, 3265, 6271, 12033, 23105, 44353, 85147, 163445, 313777, 602353, 1156339, 2219809, 4261389, 8180561, 15704215, 30147333, 57873821, 111100225, 213278943, 409431169, 785984353, 1508852673, 2896541859
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(x^2)).
|
|
MATHEMATICA
|
a[0] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 35}]
nmax = 35; A[_] = 0; Do[A[x_] = 1/(1 + x - 2 x A[x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|