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 A140825 Numerators of upper right triangle of a(i,j) = Integral_{x=i..i+1} Sum_{k=0..j} A048994(j,k)*x^k. 7
 1, 1, 3, -1, 5, 23, 1, -1, 9, 55, -19, 11, -19, 251, 1901, 27, -11, 11, -27, 475, 4277, -863, 271, -191, 271, -863, 19087, 198721, 1375, -351, 191, -191, 351, -1375, 36799, 434241, -33953, 7297, -3233, 2497, -3233, 7297, -33953, 1070017, 14097247, 57281, -10625, 3969 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Denominators of the j-th column are A002790(j). Note that the fractions defined by division are not fully reduced to coprime numerator and denominator. REFERENCES P. Curtz, Intégration numérique des systèmes différentiels à conditions initiales, Centre de Calcul Scientifique de l'Armement, Arcueil, 1969. LINKS EXAMPLE The array a(i,j) starts with rows i>=0 and columns j>=0 as: 1 1/2 -1/6 1/4 -19/30 9/4 -863/84 1375/24 ... 1 3/2 5/6 -1/4 11/30 -11/12 271/84 -117/8 ... 1 5/2 23/6 9/4 -19/30 11/12 -191/84 191/24 ... 1 7/2 53/6 55/4 251/30 -9/4 271/84 -191/24 ... 1 9/2 95/6 161/4 1901/30 475/12 -863/84 117/8 ... 1 11/2 149/6 351/4 6731/30 4277/12 19087/84 -1375/24 ... The sequence lists the numerators of the j-th column from row 0 down to row j. The fractions of the j=5 column, 9/4, -11/12, 11/12, -9/4, 475/12, 4277/12, are listed with a common denominator A002790(5)=12 as 27, -11, 11, -27, 475, 4277. MATHEMATICA a[i_, j_] := Sum[((1+i)^(k+1)-i^(k+1))*StirlingS1[j, k]/(k+1), {k, 0, j}]; col[j_] := Total[Table[a[i, j], {i, 0, j} ]*x^Range[0, j]] // Together // Numerator // CoefficientList[#, x]&; Table[col[j], {j, 0, 9}] // Flatten (* Jean-François Alcover, Jan 10 2016 *) CROSSREFS Cf. A002790, A048994, A140811. Sequence in context: A104053 A187369 A039512 * A265981 A037280 A324204 Adjacent sequences:  A140822 A140823 A140824 * A140826 A140827 A140828 KEYWORD sign,frac,tabl AUTHOR Paul Curtz, Jul 17 2008 EXTENSIONS Edited by R. J. Mathar, Aug 06 2008 STATUS approved

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Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)