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A349011 G.f. A(x) satisfies: A(x) = (1 - x * A(-x)) / (1 - 2 * x * A(x)). 1
1, 1, 5, 17, 105, 433, 2925, 13185, 93425, 443009, 3233205, 15840209, 117950745, 591187953, 4466545245, 22766535297, 173906505825, 897941153665, 6918379345125, 36089242700049, 279988660639305, 1472715584804529, 11490841104036045, 60857608450349313, 477104721264920145 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

FORMULA

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

MAPLE

A349011 := proc(n)

option remember ;

if n = 0 then

1;

else

(-1)^n*procname(n-1)+2*add(procname(k)*procname(n-k-1), k=0..n-1) ;

end if;

end proc:

seq(A349011(n), n=0..40) ; # R. J. Mathar, Aug 19 2022

MATHEMATICA

nmax = 24; A[_] = 0; Do[A[x_] = (1 - x A[-x])/(1 - 2 x A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[0] = 1; a[n_] := a[n] = (-1)^n a[n - 1] + 2 Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]

CROSSREFS

Cf. A001003, A103210, A348957.

Sequence in context: A200992 A034821 A158007 * A143562 A261425 A297476

Adjacent sequences: A349008 A349009 A349010 * A349012 A349013 A349014

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 05 2021

STATUS

approved

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Last modified December 7 14:31 EST 2022. Contains 358656 sequences. (Running on oeis4.)