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A162416 G.f.: A(x) = exp( Sum_{n>=1} A162415(n)^2*x^n/n ) where A162415 is defined by: Sum_{n>=0} x^(2^n-1) = exp( Sum_{n>=1} A162415(n)*x^n/n ). 2
1, 1, 1, 6, 12, 19, 48, 147, 305, 628, 1607, 3748, 8140, 18779, 44521, 102625, 233230, 540343, 1254459, 2877651, 6614799, 15288779, 35283125, 81210949, 187173219, 431917054, 995565240, 2293851990, 5288703013, 12194473395, 28108088241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..30.

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 +...

log(A(x)) = x + x^2/2 + 4^2*x^3/3 + 5^2*x^4/4 + 6^2*x^5/5 + 10^2*x^6/6 +...

where the coefficients are the squares of the coefficients in L(x):

L(x) = log(1 + x + x^3 + x^7 + x^15 +...+ x^(2^n-1) +...);

L(x) = x - x^2/2 + 4*x^3/3 - 5*x^4/4 + 6*x^5/5 - 10*x^6/6 + 22*x^7/7 -+...

PROG

(PARI) {a(n)=local(L=Vec(log(sum(m=0, #binary(n), x^(2^m-1))+x*O(x^n)))); polcoeff(exp(sum(k=1, n, L[k]^2*k*x^k)+x*O(x^n)), n)}

CROSSREFS

Cf. A162415.

Sequence in context: A256977 A087883 A218438 * A233586 A332543 A235268

Adjacent sequences:  A162413 A162414 A162415 * A162417 A162418 A162419

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 02 2009

STATUS

approved

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Last modified July 10 14:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)