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A111963 Inverse of renewal array for central trinomial numbers. 2
1, -1, 1, -1, -2, 1, 3, -1, -3, 1, 1, 8, 0, -4, 1, -9, -3, 14, 2, -5, 1, 1, -26, -15, 20, 5, -6, 1, 27, 27, -45, -37, 25, 9, -7, 1, -13, 76, 98, -56, -70, 28, 14, -8, 1, -81, -135, 108, 228, -46, -114, 28, 20, -9, 1, 67, -202, -459, 48, 420, 0, -168, 24, 27, -10, 1, 243, 567, -135, -1035, -210, 662, 98, -230, 15, 35, -11, 1, -285 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums have g.f. 1/sqrt(1+4x^2) [alternating sign central binomial numbers with interpolated zeros]. Diagonal sums are A111964. Inverse of A111960. Factors as (1/sqrt(1+4x^2),x/sqrt(1+4x^2))*(1/(1+x),x/(1+x)).

LINKS

Table of n, a(n) for n=0..78.

FORMULA

Riordan array (1/(sqrt(1+4x^2)+x), x/(sqrt(1+4x^2)+x)); Number triangle T(n, k)=sum{i=0..floor(n/2), C(2i+k-n-1, k)*C((2i-n-1)/2, i)(-1)^n*4^i}.

EXAMPLE

Triangle begins

1;

-1,1;

-1,-2,1;

3,-1,-3,1;

1,8,0,-4,1;

-9,-3,14,2,-5,1;

1,-26,-15,20,5,-6,1;

CROSSREFS

Sequence in context: A108415 A278572 A136644 * A206923 A078079 A176982

Adjacent sequences:  A111960 A111961 A111962 * A111964 A111965 A111966

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Aug 23 2005

STATUS

approved

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Last modified July 23 20:56 EDT 2019. Contains 325265 sequences. (Running on oeis4.)