The On-Line Encyclopedia of Integer Sequences (OEIS)

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A307374

G.f. A(x) satisfies: A(x) = 1 + x - x^2*A(x)^2.
(history; published version)

#6 by Susanna Cuyler at Sun Apr 07 00:00:23 EDT 2019

STATUS

proposed

approved

#5 by Ilya Gutkovskiy at Sat Apr 06 04:45:35 EDT 2019

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Sat Apr 06 04:41:46 EDT 2019

FORMULA

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

#3 by Ilya Gutkovskiy at Sat Apr 06 04:22:49 EDT 2019

NAME

allocated for Ilya Gutkovskiy

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

DATA

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

FORMULA

a(0) = a(1) = 1; for n > 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.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Apr 06 2019

STATUS

approved

editing

#2 by Ilya Gutkovskiy at Sat Apr 06 04:22:49 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved