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A299069 Expansion of Product_{k>=1} (1 + x^k)^phi(k), where phi() is the Euler totient function (A000010). 9
1, 1, 1, 3, 4, 8, 11, 19, 30, 44, 69, 103, 157, 229, 341, 491, 722, 1038, 1488, 2128, 3015, 4267, 5989, 8407, 11713, 16289, 22523, 31097, 42729, 58569, 80003, 108957, 147983, 200383, 270693, 364631, 490105, 656961, 878775, 1172653, 1561626, 2074982, 2751648, 3641536, 4810009, 6341365, 8344967 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

N. J. A. Sloane, Transforms

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A000010(k).

a(n) ~ exp(3^(5/3) * Zeta(3)^(1/3) * n^(2/3) / (2*Pi^(2/3))) * Zeta(3)^(1/6) / (2^(1/3) * 3^(1/6) * Pi^(5/6) * n^(2/3)). - Vaclav Kotesovec, Mar 23 2018

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

      binomial(numtheory[phi](i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..50);  # Alois P. Heinz, Mar 09 2018

MATHEMATICA

nmax = 46; CoefficientList[Series[Product[(1 + x^k)^EulerPhi[k], {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d EulerPhi[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 46}]

CROSSREFS

Cf. A000010, A061255, A107742, A159929, A192065, A318975.

Sequence in context: A212549 A212550 A024786 * A097497 A279328 A006167

Adjacent sequences:  A299066 A299067 A299068 * A299070 A299071 A299072

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 09 2018

STATUS

approved

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Last modified April 19 10:45 EDT 2019. Contains 322255 sequences. (Running on oeis4.)