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A162580
G.f.: A(x) = exp( 2*Sum_{n>=1} 2^[A007814(n)^2] * x^n/n ), where A007814(n) = exponent of highest power of 2 dividing n.
3
1, 2, 4, 6, 16, 26, 44, 62, 240, 418, 756, 1094, 2544, 3994, 6556, 9118, 32352, 55586, 99492, 143398, 330000, 516602, 845900, 1175198, 3452112, 5729026, 9953556, 14178086, 31076592, 47975098, 77547580, 107120062, 298608832, 490097602
OFFSET
0,2
LINKS
EXAMPLE
G.f.: A(x) = 1 + 2*x + 4*x^2 + 6*x^3 + 16*x^4 + 26*x^5 + 44*x^6 + ...
log(A(x))/2 = 2^0*x + 2^1*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^1*x^6/6 + 2^0*x^7/7 + 2^9*x^8/8 + ... + 2^[A007814(n)^2]*x^n/n + ...
MATHEMATICA
nmax = 500; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(IntegerExponent[k, 2]^2 + 1)*q^k/k, {k, 1, nmax}]], {q, 0, nmax}], n]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jul 04 2018 *)
PROG
(PARI) {a(n)=local(L=sum(m=1, n, 2*2^(valuation(m, 2)^2)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2009
STATUS
approved