Search: id:A035324
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%I A035324
%S A035324 1,3,1,10,6,1,35,29,9,1,126,130,57,12,1,462,562,312,94,15,1,1716,2380,
%T A035324 1578,608,140,18,1,6435,9949,7599,3525,1045,195,21,1,24310,41226,35401,
%U A035324 19044,6835,1650,259,24,1,92378,169766,161052,97954,40963,12021,2450
%N A035324 A convolution triangle of numbers, generalizing Pascal's triangle A007318.
%C A035324 Replacing each '2' in the recurrence by '1' produces Pascal's triangle 
               A007318(n-1,m-1). The columns appear as A001700, A008549, A045720, 
               A045894,...
%H A035324 W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               On generalizations of Stirling number triangles</a>, J. Integer Seqs., 
               Vol. 3 (2000), #00.2.4.
%H A035324 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A035324.text">
               First 10 rows. </a>
%F A035324 a(n+1, m) = 2*(2*n+m)*a(n, m)/(n+1) + m*a(n, m-1)/(n+1), n >= m >= 1; 
               a(n, m) := 0, n<m; a(n, 0) := 0, a(1, 1)=1; G.f. for column m: ((x*c(x)/
               sqrt(1-4*x))^m)/x, where c(x) = g.f. for Catalan numbers A000108. 
               a(n, m)=: s2(3; n, m).
%F A035324 With offset 0( 0<=k<=n), T(n,k)=Sum_{j, j>=0}A039598(n,j)*binomial(j,
               k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 30 2007
%e A035324 {1}; {3,1}; {10,6,1}; {35,29,9,1};...
%Y A035324 Cf. A000108, A007318. Row sums: A049027(n), n >= 1.
%Y A035324 If offset 0 (n >= m >= 0): convolution triangle based on A001700 (central 
               binomial coeffs. of odd order).
%Y A035324 Alternating row sums give A000108 (Catalan numbers).
%Y A035324 Sequence in context: A057967 A132964 A134283 this_sequence A091965 A107056 
               A116384
%Y A035324 Adjacent sequences: A035321 A035322 A035323 this_sequence A035325 A035326 
               A035327
%K A035324 easy,nice,nonn,tabl
%O A035324 1,2
%A A035324 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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