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A304964 Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)). 2
1, 1, 5, 13, 47, 133, 443, 1333, 4263, 13143, 41419, 128791, 403815, 1259639, 3941579, 12310299, 38492034, 120271953, 375964616, 1174935195, 3672413322, 11477465221, 35872928244, 112117013835, 350417746650, 1095202995267, 3422999582632, 10698350241417, 33437065631262, 104505382585023 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Invert transform of A007426.

LINKS

Table of n, a(n) for n=0..29.

N. J. A. Sloane, Transforms

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=1} A007426(k)*x^k).

MAPLE

A:= proc(n, k) option remember; `if`(k=1, 1,

      add(A(d, k-1), d=numtheory[divisors](n)))

    end:

a:= proc(n) option remember; `if`(n=0, 1,

      add(A(j, 4)*a(n-j), j=1..n))

    end:

seq(a(n), n=0..35);  # Alois P. Heinz, May 22 2018

MATHEMATICA

nmax = 29; CoefficientList[Series[1/(1 - Sum[x^(i j k l), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}, {l, 1, nmax/i/j/k}]), {x, 0, nmax}], x]

nmax = 29; CoefficientList[Series[1/(1 - Sum[Sum[DivisorSigma[0, d] DivisorSigma[0, k/d], {d, Divisors[k]}] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[Sum[DivisorSigma[0, d] DivisorSigma[0, k/d], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 29}]

CROSSREFS

Cf. A000005, A007426, A011782, A129921, A280486, A280487, A304963.

Sequence in context: A217892 A194639 A152925 * A120790 A162563 A250133

Adjacent sequences:  A304961 A304962 A304963 * A304965 A304966 A304967

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 22 2018

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)