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Search: id:A147315
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| 1, 1, 1, 2, 3, 1, 5, 11, 6, 1, 16, 45, 35, 10, 1, 61, 211, 210, 85, 15, 1, 272, 1113, 1351, 700, 175, 21, 1, 1385, 6551, 9366, 5901, 1890, 322, 28, 1, 7936, 42585, 70055, 51870, 20181, 4410, 546, 36, 1, 50521, 303271
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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This is the inverse of the coefficient array for the orthogonal polynomials p(n,x)
defined by: p(n,x)=if(n=-1,0,if(n=0,1,(x-n)p(n-1,x)-C(n,2)p(n-2,x))).
The Hankel array H for A000111(n+1) satisfies H=L*D*U with U the transpose of L.
Row sums are A000772(n+1) with e.g.f. dif(exp(-1)exp(sec(x)+tan(x)),x).
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EXAMPLE
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Triangle begins
1,
1, 1,
2, 3, 1,
5, 11, 6, 1,
16, 45, 35, 10, 1,
61, 211, 210, 85, 15, 1,
272, 1113, 1351, 700, 175, 21, 1
The production array for L is the tri-diagonal array
1, 1,
1, 2, 1,
0, 3, 3, 1,
0, 0, 6, 4, 1,
0, 0, 0, 10, 5, 1,
0, 0, 0, 0, 15, 6, 1,
0, 0, 0, 0, 0, 21, 7, 1,
0, 0, 0, 0, 0, 0, 28, 8, 1,
0, 0, 0, 0, 0, 0, 0, 36, 9, 1
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CROSSREFS
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Sequence in context: A089302 A049020 A144634 this_sequence A085853 A137211 A083855
Adjacent sequences: A147312 A147313 A147314 this_sequence A147316 A147317 A147318
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 05 2008
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