A145622 Denominator of the polynomial A_i(x) = Sum_{d=1..i-1} x^(i-d)/d for index i=2n+1 evaluated at x=7.

2, 12, 20, 40, 72, 792, 10296, 102960, 583440, 11085360, 3695120, 254963280, 1274816400, 11473347600, 332727080400, 20629078984800, 20629078984800, 20629078984800, 763275922437600, 763275922437600, 31294312819941600

Offset

1,1

Comments

For numerators see A145621. For general properties of A_i(x) see A145609.

Links

Table of n, a(n) for n=1..21.

Example

For n=1, i=3, so the polynomial is Sum_{d=1..2} x^(3-d)/d = x^2/1 + x^1/2 = x^2 + x/2. Setting x=7 gives 49 + 7/2 = 105/2, so a(n)=2. - Michael B. Porter, Nov 20 2025

Mathematica

m = 7; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa

Crossrefs

Cf. A145609 - A145640.

Sequence in context: A226399 A353399 A121859 * A266050 A291698 A174478

Adjacent sequences: A145619 A145620 A145621 * A145623 A145624 A145625

Keyword

frac,nonn

Author

Artur Jasinski, Oct 14 2008

Extensions

Edited by R. J. Mathar, Aug 21 2009

Status

approved