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A162582 G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^n * x^n/n ), where A006519(n) = highest power of 2 dividing n. 3
1, 2, 6, 10, 146, 282, 826, 1370, 4204986, 8408602, 25223066, 42037530, 615687706, 1189337882, 3483938586, 5778539290, 2305851850537847066, 4611703695297154842, 13835111074334385946, 23058518453371617050 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..450

EXAMPLE

G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 146*x^4 + 282*x^5 + 826*x^6 + ...

log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^8*x^4/4 + 2^0*x^5/5 + 2^6*x^6/6 + 2^0*x^7/7 + 2^24*x^8/8 + ... + A006519(n)^n*x^n/n + ...

MATHEMATICA

nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(k*IntegerExponent[k, 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))^m*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

CROSSREFS

Cf. A162580, A162581, A155200, A006519, A000123.

Sequence in context: A083458 A124621 A065799 * A123098 A136699 A033710

Adjacent sequences:  A162579 A162580 A162581 * A162583 A162584 A162585

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 06 2009

STATUS

approved

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Last modified March 25 10:16 EDT 2019. Contains 321470 sequences. (Running on oeis4.)