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A162581 G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n. 4
1, 2, 6, 10, 26, 42, 86, 130, 258, 386, 694, 1002, 1754, 2506, 4134, 5762, 9346, 12930, 20198, 27466, 42330, 57194, 85750, 114306, 169602, 224898, 326934, 428970, 618138, 807306, 1144390, 1481474, 2084610, 2687746, 3732422, 4777098, 6591386 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

EXAMPLE

G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 26*x^4 + 42*x^5 + 86*x^6 + ...

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

MATHEMATICA

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

CROSSREFS

Cf. A162580, A162582, A006519, A000123.

Sequence in context: A055237 A057434 A217381 * A061547 A218791 A320429

Adjacent sequences:  A162578 A162579 A162580 * A162582 A162583 A162584

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 06 2009

STATUS

approved

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Last modified December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)