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Search: id:A104556
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| A104556 |
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Matrix inverse of triangle A001497 of Bessel polynomials, read by rows; essentially the same as triangle A096713 of modified Hermite polynomials. |
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+0
1
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| 1, -1, 1, 0, -3, 1, 0, 3, -6, 1, 0, 0, 15, -10, 1, 0, 0, -15, 45, -15, 1, 0, 0, 0, -105, 105, -21, 1, 0, 0, 0, 105, -420, 210, -28, 1, 0, 0, 0, 0, 945, -1260, 378, -36, 1, 0, 0, 0, 0, -945, 4725, -3150, 630, -45, 1, 0, 0, 0, 0, 0, -10395, 17325, -6930, 990, -55, 1, 0, 0, 0, 0, 0, 10395, -62370, 51975, -13860, 1485, -66, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are found in A001464 (offset 1). Absolute row sums equal A000085.
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LINKS
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H. Han and S. Seo, Combinatorial proofs of inverse relations and log-concavity for Bessel numbers, Eur. J. Combinat. 29 (7) (2008) 1544-1554. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 20 2009]
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EXAMPLE
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Rows begin:
1;
-1,1;
0,-3,1;
0,3,-6,1;
0,0,15,-10,1;
0,0,-15,45,-15,1;
0,0,0,-105,105,-21,1;
0,0,0,105,-420,210,-28,1;
0,0,0,0,945,-1260,378,-36,1;
0,0,0,0,-945,4725,-3150,630,-45,1; ...
The columns being equal in absolute value to
the rows of the matrix inverse A001497:
1;
1,1;
3,3,1;
15,15,6,1;
105,105,45,10,1;
945,945,420,105,15,1; ...
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CROSSREFS
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Cf. A096713, A001497, A001464, A000085.
Sequence in context: A036870 A036874 A049403 this_sequence A116089 A122016 A067882
Adjacent sequences: A104553 A104554 A104555 this_sequence A104557 A104558 A104559
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 14 2005
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