Search: id:A109692
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%I A109692
%S A109692 1,1,1,1,4,3,1,9,23,15,1,16,86,176,105,1,25,230,950,1689,945,1,36,505,
%T A109692 3480,12139,19524,10395,1,49,973,10045,57379,177331,264207,135135,1,
%U A109692 64,1708,24640,208054,1038016,2924172,4098240,2027025,1,81,2796,53676
%N A109692 Triangle of coefficients in expansion of (1+x)(1+3x)(1+5x)(1+7x)...(1+(2n-1)x).
%C A109692 Triangle T(n,k),0<=k<=n, read by rows, given by [1, 0, 1, 0, 1, 0, 1, 
               0, 1, ...] DELTA [1, 2, 3, 4, 5, 6, 7, 8, 9, ...] where DELTA is 
               the operator defined in A084938.
%F A109692 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%F A109692 a(n, m) = a(n-1,m)+(2*n-1)*a(n-1,m-1) with a(n, n) = (2*n-1)!! and a(n, 
               0) = 1.
%F A109692 (End)
%e A109692 1; 1, 1; 1, 4, 3; 1, 9, 23, 15; 1, 16, 86, 176, 105; ...
%p A109692 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%p A109692 nmax:=8; mmax:=nmax: for n from 0 to nmax do a(n,0):=doublefactorial(2*n-1) 
               od: for n from 0 to nmax do a(n,n):=1 od: for n from 2 to nmax do 
               for m from 1 to n-1 do a(n,m) := (2*n-1)*a(n-1,m)+a(n-1,m-1) od; 
               od: T:=0; for n from 0 to nmax do for m from 0 to n do a(T):=a(n,
               n-m); T:=T+1 od: od: seq(a(n),n=0..T-1);
%p A109692 (End)
%Y A109692 A039758 is signed version. A028338 transposed.
%Y A109692 Diagonals : A000012, A000290, A024196, A024197, A024198; A001147, A004041, 
               A028339, A028340, A028341 . Row sums : A000165.
%Y A109692 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%Y A109692 A161198 is a transposed scaled triangle version.
%Y A109692 (End)
%Y A109692 Sequence in context: A165732 A123160 A039758 this_sequence A157894 A128813 
               A109062
%Y A109692 Adjacent sequences: A109689 A109690 A109691 this_sequence A109693 A109694 
               A109695
%K A109692 nonn,tabl
%O A109692 0,5
%A A109692 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 08 2005

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