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A060184 Triangle of generalized sum of divisors function, read by rows. 4
1, 0, 1, 2, 0, -1, 1, 2, 1, 2, 0, 0, 1, 2, 1, 1, -2, 0, 1, 3, 1, 5, 6, 0, 0, -1, -1, 2, 1, 5, 5, -2, 0, -2, -3, 2, 2, 9, 10, 0, 1, 4, 3, 0, 4, 0, 2, 9, 9, -3, 1, 3, -2, -7, 2, 0, 3, 14, 16, 0, 2, 6, -1, -9, 2, 0, 3, 15, 17, -2, 1, 8, 19, 10, -6, 4, 0, -1, 0, 15, 22, 0, 1, 9, 21, 7, -13, 2, 0, -2, -4, 11, 20, -4, 2, 15, 33, 14, -15, 3, 0, -4, -10, 10, 28, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).

REFERENCES

P. A. MacMahon, Divisors of numbers and their continuations in the theory of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.

LINKS

Table of n, a(n) for n=1..107.

FORMULA

G.f. for k-th diagonal (the k-th row of the sideways triangle shown in the example): Sum_{ m_1 < m_2 < ... < m_k} q^(m_1+m_2+...+m_k)/((1+q^m_1)*(1+q^m_2)*...*(1+q^m_k)) = Sum_n T(n, k)*q^n.

EXAMPLE

Triangle turned on its side begins:

  1  0  2 -1  2  0  2 -2  3  0  2 ...

        1  0  1  2  1  1  1  6 -1 ...

              1  0  1  0  5 -1  5 ...

MATHEMATICA

max = 27(*rows*); t[n_, k_] := Module[{m, mm, q, s}, mm = Array[m, k]; s = Sum[q^Total[mm]/Times @@ (1+q^mm), Evaluate[Sequence @@ Transpose[{mm, Join[{1}, Most[mm]+1], max-Range[k-1, 0, -1]}]]]; SeriesCoefficient[s, {q, 0, n}]]; Table[Print[an = Table[t[n, k], {k, Floor[(Sqrt[8*n+1]-1)/2], 1, -1}]]; an, {n, 1, max}] // Flatten (* Jean-Fran├žois Alcover, Jan 21 2014 *)

CROSSREFS

Diagonals give A048272, A060185, A060186.

Cf. A060043, A060044, A060047, A060177.

Sequence in context: A116374 A181953 A025911 * A055639 A156542 A066360

Adjacent sequences:  A060181 A060182 A060183 * A060185 A060186 A060187

KEYWORD

sign,tabf,easy,nice

AUTHOR

N. J. A. Sloane, Mar 20 2001

EXTENSIONS

More terms from Vladeta Jovovic, Sep 20 2007

STATUS

approved

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Last modified October 20 11:17 EDT 2018. Contains 316379 sequences. (Running on oeis4.)