A307374 G.f. A(x) satisfies: A(x) = 1 + x - x^2*A(x)^2.

1, 1, -1, -2, 1, 6, 1, -18, -16, 50, 93, -112, -428, 98, 1713, 936, -6004, -8382, 17512, 47608, -33826, -221936, -36335, 892164, 862666, -3051022, -6076072, 8026380, 32247334, -8222288, -144487267, -81500652, 555489738, 801700858, -1751543424, -4898513044

Offset

0,4

Links

Table of n, a(n) for n=0..35.

Formula

a(0) = a(1) = 1; a(n+2) = -Sum_{k=0..n} a(k)*a(n-k).

Example

G.f.: A(x) = 1 + x - x^2 - 2*x^3 + x^4 + 6*x^5 + x^6 - 18*x^7 - 16*x^8 + 50*x^9 + 93*x^10 - 112*x^11 - 428*x^12 + ...

Mathematica

terms = 35; A[_] = 0; Do[A[x_] = 1 + x - x^2 A[x]^2 + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = -Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 35}]

Crossrefs

Cf. A007477, A104565.

Sequence in context: A280736 A279095 A186283 * A173279 A277440 A321597

Adjacent sequences: A307371 A307372 A307373 * A307375 A307376 A307377

Keyword

sign

Author

Ilya Gutkovskiy, Apr 06 2019

Status

approved