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A304964 Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)). 2

%I

%S 1,1,5,13,47,133,443,1333,4263,13143,41419,128791,403815,1259639,

%T 3941579,12310299,38492034,120271953,375964616,1174935195,3672413322,

%U 11477465221,35872928244,112117013835,350417746650,1095202995267,3422999582632,10698350241417,33437065631262,104505382585023

%N Expansion of 1/(1 - Sum_{i>=1, j>=1, k>=1, l>=1} x^(i*j*k*l)).

%C Invert transform of A007426.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

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

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

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

%p end:

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

%p add(A(j, 4)*a(n-j), j=1..n))

%p end:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, May 22 2018

%t 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]

%t 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]

%t 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}]

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 22 2018

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)