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Search: id:A119274
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| A119274 |
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Triangle of coefficients of numerators in Pade approximation to exp(x). |
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+0
3
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| 1, 2, 1, 12, 6, 1, 120, 60, 12, 1, 1680, 840, 180, 20, 1, 30240, 15120, 3360, 420, 30, 1, 665280, 332640, 75600, 10080, 840, 42, 1, 17297280, 8648640, 1995840, 277200, 25200, 1512, 56, 1, 518918400, 259459200, 60540480, 8648640, 831600, 55440, 2520
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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n-th numerator of Pade approximation is (1/n!)*sum{j=0..n, C(n,j)(2n-j)!x^j}. Reversal of A113025. Row sums are A001517. First column is A001813. Inverse is A119275.
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FORMULA
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Number triangle T(n,k)=C(n,k)(2n-k)!/n!
After adding a leading column (1,0,0,0,...), the triangle gives the coefficients of the Sheffer associated sequence (binomial-type polynomials) for the delta (lowering) operator D(1-D) with e.g.f. exp[ x * (1 - sqrt(1-4t)) / 2 ] . See Mathworld on Sheffer sequences. See A134685 for relation to Catalan numbers. - Tom Copeland (tcjpn(AT)msn.com), Feb 09 2008
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EXAMPLE
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Triangle begins
1,
2, 1,
12, 6, 1,
120, 60, 12, 1,
1680, 840, 180, 20, 1,
30240, 15120, 3360, 420, 30, 1
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CROSSREFS
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Cf. A001497.
Sequence in context: A048743 A049055 A008285 this_sequence A066991 A132875 A050139
Adjacent sequences: A119271 A119272 A119273 this_sequence A119275 A119276 A119277
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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), May 12 2006
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