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A124433 Irregular array {a(n,m)} read by rows where (sum{n>=1} sum{m=1 to A001222(n)+1} a(n,m)*y^m/n^x) = 1/(zeta(x)-1+1/y) for all x and y where the double sum converges. 0
1, 0, -1, 0, -1, 0, -1, 1, 0, -1, 0, -1, 2, 0, -1, 0, -1, 2, -1, 0, -1, 1, 0, -1, 2, 0, -1, 0, -1, 4, -3, 0, -1, 0, -1, 2, 0, -1, 2, 0, -1, 3, -3, 1, 0, -1, 0, -1, 4, -3, 0, -1, 0, -1, 4, -3, 0, -1, 2, 0, -1, 2, 0, -1, 0, -1, 6, -9, 4, 0, -1, 1, 0, -1, 2, 0, -1, 2, -1, 0, -1, 4, -3, 0, -1, 0, -1, 6, -6, 0, -1, 0, -1, 4, -6, 4, -1, 0, -1, 2, 0, -1, 2, 0, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Row n has A001222(n)+1 terms. The polynomial P_n(y) = (sum{m=1 to A001222(n)+1} a(n,m)*y^m) is a generalization of the Mobius (Moebius) function, where P_n(1) = A008683(n).

REFERENCES

Mohammad K. Azarian, A Double Sum, Problem 440, College Mathematics Journal, Vol. 21, No. 5, Nov. 1990, p. 424.  Solution published in Vol. 22. No. 5, Nov. 1991, pp. 448-449.

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(1,1)=1. a(n,1) = 0 for n>=2. a(n,m+1) = -sum{k|n,k < n} a(k,m), where, for the purpose of this sum, a(k,m) = 0 if m > A001222(k)+1.

EXAMPLE

1/(zeta(x) - 1 + 1/y) = y - y^2/2^x - y^2/3^x + ( - y^2 + y^3)/4^x - y^2/5^x + ( - y^2 + 2y^3)/6^x - y^2/7^x + ...

MATHEMATICA

f[l_List] := Block[{n = Length[l] + 1, c}, c = Plus @@ Last /@ FactorInteger[n]; Append[l, Prepend[ -Plus @@ Pick[PadRight[ #, c] & /@ l, Mod[n, Range[n - 1]], 0], 0]]]; Nest[f, {{1}}, 34] // Flatten(* Ray Chandler, Feb 13 2007 *)

CROSSREFS

Cf. A008683, A001222.

Sequence in context: A054528 A025884 A257024 * A287104 A190483 A090239

Adjacent sequences:  A124430 A124431 A124432 * A124434 A124435 A124436

KEYWORD

sign,tabf

AUTHOR

Leroy Quet, Dec 15 2006

EXTENSIONS

Extended by Ray Chandler, Feb 13 2007

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)