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 A116395 Riordan array (1/sqrt(1-4x), (1/sqrt(1-4x)-1)/2). 7

%I

%S 1,2,1,6,5,1,20,22,8,1,70,93,47,11,1,252,386,244,81,14,1,924,1586,

%T 1186,500,124,17,1,3432,6476,5536,2794,888,176,20,1,12870,26333,25147,

%U 14649,5615,1435,237,23,1,48620,106762,112028,73489,32714,10135,2168,307,26,1

%N Riordan array (1/sqrt(1-4x), (1/sqrt(1-4x)-1)/2).

%C Row sums are A007854. Diagonal sums are A116396.

%C Triangle T(n,k), 0<=k<=n, read by rows given by [2,1,1,1,1,1,1,...] DELTA [1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - _Philippe Deléham_, Jun 05 2007

%C Inverse of Riordan array (1/(1+2x), x(1+x)/(1+2x)^2) (see A123876). - _Philippe Deléham_, Oct 25 2007

%F Number triangle T(n,k)=(4^n/2^k)*sum{j=0..k, C(k,j)C(n+(j-1)/2,n)(-1)^(k-j)}

%F Sum_{k, 0<=k<=n}(-1)^k*T(n,k)=A000108(n), Catalan numbers . - _Philippe Deléham_, Nov 07 2006

%F T(n,k)=Sum_{j, j>=0}A039599(n,j)*binomial(j,k). - _Philippe Deléham_, Mar 30 2007

%F Sum_{k, 0<=k<=n}T(n,k)*x^k = A127053(n), A126985(n), A127016(n), A127017(n), A126987(n), A126986(n), A126982(n), A126984(n), A126983(n), A000007(n), A000108(n), A000984(n), A007854(n), A076035(n), A076036(n), A127628(n), A126694(n), A115970(n) for x = -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 respectively . - _Philippe Deléham_, Oct 25 2007

%e Triangle begins

%e 1,

%e 2, 1,

%e 6, 5, 1,

%e 20, 22, 8, 1,

%e 70, 93, 47, 11, 1,

%e 252, 386, 244, 81, 14, 1

%K easy,nonn,tabl

%O 0,2

%A _Paul Barry_, Feb 12 2006

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Last modified October 17 05:23 EDT 2018. Contains 316275 sequences. (Running on oeis4.)