|
| |
|
|
A165313
|
|
Triangle T(n,k) = A091137(k-1) read by rows.
|
|
3
| |
|
|
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; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| 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 up to 6)). See A147998. Vertical numerators:A000027,A147998,A152064,A157371,A165281.
|
|
|
REFERENCES
| P. Curtz, Integration numerique des systemes differentiels a conditions initiales, Centre de Calcul Scientifique de l'Armement, Note 12, Arcueil, (1969).
|
|
|
EXAMPLE
| 1;
1,2;
1,2,12;
1,2,12,24;
1,2,12,24,710;
|
|
|
CROSSREFS
| Sequence in context: A062345 A077098 A069238 * A052579 A153908 A048296
Adjacent sequences: A165310 A165311 A165312 * A165314 A165315 A165316
|
|
|
KEYWORD
| nonn,tabl,uned
|
|
|
AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Sep 14 2009
|
| |
|
|
