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Search: id:A110506
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| A110506 |
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Riordan array (1/(1-xc(2x)),xc(2x)/(1-xc(2x))), c(x) the g.f. of A000108. |
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+0
6
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| 1, 1, 1, 3, 4, 1, 13, 19, 7, 1, 67, 102, 44, 10, 1, 381, 593, 278, 78, 13, 1, 2307, 3640, 1795, 568, 121, 16, 1, 14589, 23231, 11849, 4051, 999, 173, 19, 1, 95235, 152650, 79750, 28770, 7820, 1598, 234, 22, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Deleham triangle Delta(0^n,2-0^n) [see construction in A084938]. The binomial transform of the inverse of this triangle has general element (-2)^(n-k)*C(k,n-k), that is, it is the Riordan array (1,x(1-2x)) [A110509]. Row sums are A052701. Diagonal sums are A110508. Inverse is A110511.
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FORMULA
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Number triangle T(0, k)=0^k, T(n, k)=sum{j=0..n, j*C(2n-j-1, n-j)C(j, k)2^(n-j)}, n, k>0.
T(n,k)=(-1)^(n-k)*A114189(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 24 2007
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EXAMPLE
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Rows begin
1;
1,1;
3,4,1;
13,19,7,1;
67,102,44,10,1;
381,593,278,78,13,1;
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CROSSREFS
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Sequence in context: A109956 A123319 A076785 this_sequence A114189 A059110 A100326
Adjacent sequences: A110503 A110504 A110505 this_sequence A110507 A110508 A110509
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 24 2005
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