A163572 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2*A006519(n)*x)^n * x^n/n ) where A006519(n) is the highest power of 2 dividing n.

1, 1, 3, 7, 19, 39, 169, 765, 2183, 4131, 11561, 55157, 666381, 8175433, 68536455, 355280675, 1048740623, 1931107235, 5055100985, 13108206741, 38734589993, 143320957605, 1022112572635, 26523801989399, 914332703582521

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 39*x^5 + 169*x^6 +...
log(A(x)) = (1+2*x)*x + (1+4*x)^2*x^2/2 + (1+2*x)^3*x^3/3 + (1+8*x)^4*x^4/4 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (1+2^valuation(2*m, 2)*x+x*O(x^n))^m*x^m/m)), n)}

Crossrefs

Cf. A156100, A159308, A163189.

Sequence in context: A239416 A281866 A173114 * A292775 A282024 A356617

Adjacent sequences: A163569 A163570 A163571 * A163573 A163574 A163575

Keyword

nonn

Author

Paul D. Hanna, Jul 31 2009

Status

approved