

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
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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)^(nk)*T(n,k).
The Riordan array (1,x/sqrt(14*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(14x^2), x/sqrt(14x^2)); Number triangle T(n, k)=(1+(1)^(nk))*binomial((n1)/2, (nk)/2)*2^(nk)/2.
G.f.: 1/(1xy2x^2/(1x^2/(1x^2/(1x^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



