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A143019 Infinite square array read by antidiagonals: a(q,n)=is the coefficient of z^n in the series expansion of C(z)^q/(1-4z)^(3/2), where C(z)=[1-sqrt(1-4z)]/(2z) is the Catalan function (q,n=0,1,2,...). 0

%I

%S 1,1,6,1,7,30,1,8,38,140,1,9,47,187,630,1,10,57,244,874,2772,1,11,68,

%T 312,1186,3958,12012,1,12,80,392,1578,5536,17548,51480,1,13,93,485,

%U 2063,7599,25147,76627,218790,1,14,107,592,2655,10254,35401,112028,330818

%N Infinite square array read by antidiagonals: a(q,n)=is the coefficient of z^n in the series expansion of C(z)^q/(1-4z)^(3/2), where C(z)=[1-sqrt(1-4z)]/(2z) is the Catalan function (q,n=0,1,2,...).

%C a(q,n)=a(q-1,n)+a(q+1,n-1).

%C Row 0 is A002457; row 1 is A000531; row 2 is A029760; row 3 is A045720.

%F a(q,n)=Sum(4^i*binom(2n-2i+q,n-i), i=0..n).

%e Array starts:

%e 1 6 30 140 630 ...

%e 1 7 38 187 874 ...

%e 1 8 47 244 1186 ...

%e 1 9 57 312 1578 ...

%e .......

%e .......

%p a:=proc(q,n) options operator, arrow: sum(4^i*binomial(2*n-2*i+q, n-i), i= 0.. n) end proc: aa:=proc(q,n) options operator, arrow: a(q-1,n-1) end proc: matrix(10,10,aa); # yields sequence in matrix form

%Y Cf. A002457, A000531, A029760, A045720.

%K nonn,tabl

%O 0,3

%A _Emeric Deutsch_, Jul 24 2008

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Last modified January 17 06:34 EST 2019. Contains 319207 sequences. (Running on oeis4.)