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Search: id:A118384
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| A118384 |
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Guassian column reduction of Hankel matrix for central Delannoy numbers. |
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+0
1
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| 1, 3, 1, 13, 6, 1, 63, 33, 9, 1, 321, 180, 62, 12, 1, 1683, 985, 390, 100, 15, 1, 8989, 5418, 2355, 720, 147, 18, 1, 48639, 29953, 13923, 4809, 1197, 203, 21, 1, 265729, 166344, 81340, 30744, 8806, 1848, 268, 24, 1, 1462563, 927441, 471852, 191184, 60858
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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First column is central Delannoy numbers A001850. Second column is A050151.
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REFERENCES
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P. Peart and W.-J. Woan, Generating Functions via Hankel and Stieltjes Matrices, Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.1
W.-J. Woan, Hankel Matrices and Lattice Paths, Journal of Integer Sequences, Vol. 4 (2001), Article 01.1.2
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FORMULA
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Number triangle T(n,k)=sum{j=0..n, C(n,j)C(j,n-k-j)2^(n-k-j)3^(2j-(n-k))}; Riordan array (1/sqrt(1-6x+x^2), (1-3x-sqrt(1-6x+x^2))/(4x)); Column k has e.g.f. exp(3x)Bessel_I(k,2*sqrt(2)x)/(sqrt(2))^k.
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EXAMPLE
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Triangle begins
1,
3, 1,
13, 6, 1,
63, 33, 9, 1,
321, 180, 62, 12, 1,
1683, 985, 390, 100, 15, 1
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CROSSREFS
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Sequence in context: A134768 A113139 A096773 this_sequence A133176 A089435 A088814
Adjacent sequences: A118381 A118382 A118383 this_sequence A118385 A118386 A118387
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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), Apr 26 2006
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