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Search: id:A165313
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| 1, 1, 2, 1, 2, 12, 1, 2, 12, 24, 1, 2, 12, 24, 720, 1, 2, 12, 24, 720, 1440, 1, 2, 12, 24, 720, 1440, 60480, 1, 2, 12, 24, 720, 1440, 60480, 120960, 1, 2, 12, 24, 720, 1440, 60480, 120960, 3628800, 1, 2, 12, 24, 720, 1440, 60480, 120960, 3628800, 7257600, 1, 2, 12
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Fractal. From a study of modified initialization formulas in Adams-Bashforth (1855-1883) multisteps method for numerical integration. In p.36, a(i,j) comes from (j!)*a(i,j)=Integral (from -i-1 to 1) u*(u-1)* .. *(u-j+1) du;ref p.32. Then, with i vertical,j horizontal ,with unreduced fractions, partial array i=0) 1,1/2,-1/12,1/24,-19/720,27/1440, 1) 1,3/2,5/12,-1/24, 11/720,-11/1440, 2) 1,5/2,23/12,9/24,-19/720,11/1440, 3) 1,7/2,53/12,55/24,251/720,-27/1440, 4) 1,9/2,95/12,161/24,1901/720,475/1440, 5) 1,11/2,149/12,351/24,6731/720,4277/1440, .
See A141417, A140825,A157982, horizontal numerators:A141047, vertical numerators:A000012,A005408,A141530,A157411. In page 56, coefficients are s(l,q)=(1/q!)*integral (from -l-1 to 1) u*(u+1)* .. *(u+q-1) du. Unreduced fractions array is l=-1) 1,1/2,5/12,9/24,251/720,475/1440,=A002657/A091137, 0) 2,0,4/12,8/24,232/720,448/1440, 1) 3,-3/2,9/12,9/24,243/720,459/1440, 2) 4,-8/2,32/12,0/24,224/720,448/1440, 3) 5,-15/2,85/12,-55/24, 475/720,475/1440, .. (in p.56 upto 6)). See A147998. Vertical numerators:A000027,A147998,A152064,A157371,A165281.
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REFERENCES
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P. Curtz, Integration numerique des systemes differentiels a conditions initiales, 135pages, Centre de Calcul Scientifique de l'Armement, Note 12, Arcueil, 1969.
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FORMULA
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Antidiagonal writing of denominators of arrays in pp.36 and 56 of reference.
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CROSSREFS
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Sequence in context: A062345 A077098 A069238 this_sequence A052579 A153908 A048296
Adjacent sequences: A165310 A165311 A165312 this_sequence A165314 A165315 A165316
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KEYWORD
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nonn,uned
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Sep 14 2009
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