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A191829 a(n) = Sum_{i+j+k=n, i,j,k >= 1} tau(i)*tau(j)*tau(k), where tau() = A000005(). 4
0, 0, 1, 6, 18, 41, 78, 132, 209, 306, 435, 591, 780, 1008, 1268, 1584, 1917, 2335, 2751, 3294, 3776, 4467, 5034, 5875, 6522, 7548, 8250, 9498, 10260, 11734, 12546, 14268, 15134, 17151, 18018, 20361, 21234, 23907, 24818, 27834, 28677, 32218, 32937, 36825, 37672, 41970, 42576, 47633, 48006, 53436, 54008, 59868, 60042, 67020, 66690 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is Andrews's D_{0,0,0}(n).

REFERENCES

Titchmarsh, E. C. "Some problems in the analytic theory of numbers." The Quarterly Journal of Mathematics 1 (1942): 129-152.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130.

FORMULA

G.f.: (Sum_{k>=1} x^k/(1 - x^k))^3. - Ilya Gutkovskiy, Jan 01 2017

MAPLE

with(numtheory);

D000:=proc(n) local t1, i, j;

t1:=0;

for i from 1 to n-1 do

for j from 1 to n-1 do

if (i+j < n) then t1 := t1+numtheory:-tau(i)*numtheory:-tau(j)*numtheory:-tau(n-i-j); fi;

od; od;

t1;

end;

[seq(D000(n), n=1..60)];

# second Maple program:

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

      `if`(k=1, `if`(n=0, 0, numtheory[tau](n)), (q->

       add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))

    end:

a:= n-> b(n, 3):

seq(a(n), n=1..55);  # Alois P. Heinz, Feb 01 2021

MATHEMATICA

nmax = 50; Rest[CoefficientList[Series[(-1/2 + (Log[1-x] + QPolyGamma[0, 1, 1/x])/Log[x])^3, {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jan 01 2017 *)

CROSSREFS

Cf. A000005, A055507, A191831.

Sequence in context: A299263 A015224 A163983 * A023620 A074837 A286308

Adjacent sequences:  A191826 A191827 A191828 * A191830 A191831 A191832

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 17 2011

STATUS

approved

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Last modified June 15 13:47 EDT 2021. Contains 345048 sequences. (Running on oeis4.)