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A111959 Renewal array for aerated central binomial coefficients. 3
1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 6, 0, 6, 0, 1, 0, 16, 0, 8, 0, 1, 20, 0, 30, 0, 10, 0, 1, 0, 64, 0, 48, 0, 12, 0, 1, 70, 0, 140, 0, 70, 0, 14, 0, 1, 0, 256, 0, 256, 0, 96, 0, 16, 0, 1, 252, 0, 630, 0, 420, 0, 126, 0, 18, 0, 1, 0, 1024, 0, 1280, 0, 640, 0, 160, 0, 20, 0, 1, 924, 0, 2772, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A098615. Binomial transform (product with C(n,k)) is A111960. Diagonal sums are A026671 (with interpolated zeros). Inverse is (1/sqrt(1+4x^2),x/sqrt(1+4x^2)), or (-1)^(n-k)*T(n,k).

The Riordan array (1,x/sqrt(1-4*x^2)) is the same array with an additional column of zeros (besides the top element 1) added to the left. - Vladimir Kruchinin, Feb 17 2011

LINKS

Table of n, a(n) for n=0..81.

Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565

FORMULA

Riordan array (1/sqrt(1-4x^2), x/sqrt(1-4x^2)); Number triangle T(n, k)=(1+(-1)^(n-k))*binomial((n-1)/2, (n-k)/2)*2^(n-k)/2.

G.f.: 1/(1-xy-2x^2/(1-x^2/(1-x^2/(1-x^2/(1-.... (continued fraction). [From Paul Barry, Jan 28 2009]

EXAMPLE

Triangle begins

1;

0,1;

2,0,1;

0,4,0,1;

6,0,6,0,1;

0,16,0,8,0,1;

CROSSREFS

Cf. A054335.

Sequence in context: A202328 A136688 A131321 * A110109 A145973 A155761

Adjacent sequences:  A111956 A111957 A111958 * A111960 A111961 A111962

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Aug 23 2005

STATUS

approved

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Last modified June 1 18:43 EDT 2020. Contains 334762 sequences. (Running on oeis4.)