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A145621

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

105, 31087, 2538991, 248821433, 21946050833, 11828921402977, 7535022933740305, 3692161237533130831, 1025190103621701235981, 954451986471803883166747, 15589382445706130101521201, 52707702048932425873860727511, 12913387001988444339098720100139, 5694803667876903953542559254499399

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OFFSET

1,1

COMMENTS

For denominators see A145622. For general properties of A_i(x) see A145609.

LINKS

Robert Israel, Table of n, a(n) for n = 1..390

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)=105. - Michael B. Porter, Nov 20 2025

MAPLE

f:= n -> numer(add(7^(2*n+1-d)/d, d=1..2*n)):

map(f, [$1..40]); # Robert Israel, Jun 05 2016

MATHEMATICA

m = 7; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa

(* alternate program *)

a[n_, m_]:=Integrate[(m-x^n)/(m-x), {x, 0, 1}]+(m^n-m)Log[m/(m-1)]

Table[7 a[2 n, 7] // FullSimplify // Numerator, {n, 1, 25}] (* Gerry Martens, Jun 04 2016 *)

CROSSREFS

Cf. A145609 - A145640.

Sequence in context: A368513 A295463 A339847 * A167779 A275461 A054862

Adjacent sequences: A145618 A145619 A145620 * A145622 A145623 A145624