Search: id:A129818
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%I A129818
%S A129818 1,1,1,1,3,1,1,6,5,1,1,10,15,7,1,1,15,35,28,9,1,1,21,70,84,45,11,1,1,28,
%T A129818 126,210,165,66,13,1,1,36,210,462,495,286,91,15,1,1,45,330,924,1287,
%U A129818 1001,455,120,120,17,1,1,55,495,1716,3003,3003,1820,680,153,19,1
%V A129818 1,-1,1,1,-3,1,-1,6,-5,1,1,-10,15,-7,1,-1,15,-35,28,-9,1,1,-21,70,-84,
               45,-11,1,-1,28,
%W A129818 -126,210,-165,66,-13,1,1,-36,210,-462,495,-286,91,-15,1,-1,45,-330,924,
               -1287,1001,
%X A129818 -455,120,120,-17,1,1,-55,495,-1716,3003,-3003,1820,-680,153,-19,1
%N A129818 Riordan array (1/(1+x),x/(1+x)^2), inverse array is A039599 .
%C A129818 Row sums : A057078 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 
               11 2007
%D A129818 Paul Barry, A Catalan Transform and Related Transformations on Integer 
               Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%F A129818 T(n,k)=(-1)^(n-k)*A085478(n,k)= (-1)^(n-k)*binomial(n+k,2*k) .
%F A129818 Sum_{k, 0<=k<=n}T(n,k)*A000531(k)=n^2, with A000531(0)=0 . - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Jun 11 2007
%F A129818 Sum_{k, 0<=k<=n}T(n,k)*x^k = A033999(n), A057078(n), A057077(n), A057079(n), 
               A005408(n), A001906(n), A001834(n), A030221(n), A002315(n), A033890(n), 
               A057080(n), A057081(n), A054320(n), A097783(n), A077416(n), A126866(n), 
               A028230(n+1) for x = 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 respectively. 
               [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2009]
%e A129818 Triangle begins:
%e A129818 1;
%e A129818 -1, 1;
%e A129818 1, -3, 1;
%e A129818 -1, 6, -5, 1;
%e A129818 1, -10, 15, -7, 1;
%e A129818 -1, 15, -35, 28, -9, 1;
%e A129818 1, -21, 70, -84, 45, -11, 1;
%e A129818 -1, 28, -126, 210, -165, 66, -13, 1;
%e A129818 1, -36, 210, -462, 495, -286, 91, -15, 1;
%e A129818 -1, 45, -330, 924, -1287, 1001, -455, 120, -17, 1;
%e A129818 1, -55, 495, -1716, 3003, -3003, 1820, -680, 153, -19, 1 ;...
%Y A129818 Sequence in context: A103141 A085478 A123970 this_sequence A055898 A145904 
               A159572
%Y A129818 Adjacent sequences: A129815 A129816 A129817 this_sequence A129819 A129820 
               A129821
%K A129818 sign,tabl,new
%O A129818 0,5
%A A129818 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 09 2007

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