Search: id:A116395
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%I A116395
%S A116395 1,2,1,6,5,1,20,22,8,1,70,93,47,11,1,252,386,244,81,14,1,924,1586,1186,
%T A116395 500,124,17,1,3432,6476,5536,2794,888,176,20,1,12870,26333,25147,14649,
%U A116395 5615,1435,237,23,1,48620,106762,112028,73489,32714,10135,2168,307,26,
               1
%N A116395 Riordan array (1/sqrt(1-4x), (1/sqrt(1-4x)-1)/2).
%C A116395 Row sums are A007854. Diagonal sums are A116396.
%C A116395 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 DELEHAM (kolotoko(AT)wanadoo.fr), Jun 05 2007
%C A116395 Inverse of Riordan array (1/(1+2x), x(1+x)/(1+2x)^2) (see A123876). - 
               Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 25 2007
%F A116395 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 A116395 Sum_{k, 0<=k<=n}(-1)^k*T(n,k)=A000108(n), Catalan numbers . - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Nov 07 2006
%F A116395 T(n,k)=Sum_{j, j>=0}A039599(n,j)*binomial(j,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 30 2007
%F A116395 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 DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 25 2007
%e A116395 Triangle begins
%e A116395 1,
%e A116395 2, 1,
%e A116395 6, 5, 1,
%e A116395 20, 22, 8, 1,
%e A116395 70, 93, 47, 11, 1,
%e A116395 252, 386, 244, 81, 14, 1
%Y A116395 Sequence in context: A008970 A055896 A159965 this_sequence A159924 A133367 
               A121576
%Y A116395 Adjacent sequences: A116392 A116393 A116394 this_sequence A116396 A116397 
               A116398
%K A116395 easy,nonn,tabl
%O A116395 0,2
%A A116395 Paul Barry (pbarry(AT)wit.ie), Feb 12 2006

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