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A318914
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Expansion of e.g.f. Product_{p prime, k>=1} 1/(1 - x^(p^k))^(1/(p^k)).
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2
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1, 0, 1, 2, 15, 44, 475, 2274, 33313, 227240, 2920041, 26754650, 469513231, 4613913732, 85842524755, 1174844041994, 24672317426625, 334246510927184, 7985602649948113, 127351500133158450, 3282809137540001551, 60776696924693716700, 1556379682561575238731, 32568139442090869594802
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: exp(Sum_{k>=1} bigomega(k)*x^k/k), where bigomega(k) = number of prime divisors of k counted with multiplicity (A001222).
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MAPLE
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seq(n!*coeff(series(exp(add(bigomega(k)*x^k/k, k=1..100)), x=0, 24), x, n), n=0..23); # Paolo P. Lava, Jan 09 2019
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Product[1/(1 - x^k)^(Boole[PrimePowerQ[k]]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Exp[Sum[PrimeOmega[k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = (n - 1)! Sum[PrimeOmega[k] a[n - k]/(n - k)!, {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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