A140825 - OEIS

%I #14 Jan 18 2016 02:15:57

%S 1,1,3,-1,5,23,1,-1,9,55,-19,11,-19,251,1901,27,-11,11,-27,475,4277,

%T -863,271,-191,271,-863,19087,198721,1375,-351,191,-191,351,-1375,

%U 36799,434241,-33953,7297,-3233,2497,-3233,7297,-33953,1070017,14097247,57281,-10625,3969

%N Numerators of upper right triangle of a(i,j) = Integral_{x=i..i+1} Sum_{k=0..j} A048994(j,k)*x^k.

%C 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.

%D P. Curtz, Intégration numérique des systèmes différentiels à conditions initiales, Centre de Calcul Scientifique de l'Armement, Arcueil, 1969.

%e The array a(i,j) starts with rows i>=0 and columns j>=0 as:

%e 1 1/2 -1/6 1/4 -19/30 9/4 -863/84 1375/24 ...

%e 1 3/2 5/6 -1/4 11/30 -11/12 271/84 -117/8 ...

%e 1 5/2 23/6 9/4 -19/30 11/12 -191/84 191/24 ...

%e 1 7/2 53/6 55/4 251/30 -9/4 271/84 -191/24 ...

%e 1 9/2 95/6 161/4 1901/30 475/12 -863/84 117/8 ...

%e 1 11/2 149/6 351/4 6731/30 4277/12 19087/84 -1375/24 ...

%e The sequence lists the numerators of the j-th column from row 0 down to row j.

%e 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.

%t 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 *)

%Y Cf. A002790, A048994, A140811.

%K sign,frac,tabl

%O 0,3

%A _Paul Curtz_, Jul 17 2008

%E Edited by _R. J. Mathar_, Aug 06 2008