A217553 G.f.: exp( Sum_{n>=1} 4^A001511(n) * x^n/n ), where 2^A001511(n) is the highest power of 2 that divides 2*n.

1, 4, 16, 44, 128, 308, 752, 1628, 3584, 7268, 14864, 28556, 55296, 102036, 189168, 337084, 603136, 1044676, 1814288, 3064556, 5188352, 8578548, 14205936, 23041308, 37420800, 59680548, 95265552, 149620812, 235161216, 364301652, 564627952, 863725948, 1321756672

Offset: 0

Author

Paul D. Hanna, Oct 30 2012

Keywords

• nonn

Comments

Compare g.f. to the g.f. of binary partitions (A000123):

exp( Sum_{n>=1} 2^A001511(n) * x^n/n ).

Examples

			G.f.: A(x) = 1 + 4*x + 16*x^2 + 44*x^3 + 128*x^4 + 308*x^5 + 752*x^6 +...
where
log(A(x)) = 4^1*x + 4^2*x^2/2 + 4^1*x^3/3 + 4^4*x^4/4 + 4^1*x^5/5 + 4^2*x^6/6 + 4^1*x^7/7 + 4^4*x^8/8 + 4^1*x^9/9 + 4^2*x^10/10 + 4^1*x^11/11 + 4^4*x^12/12 +...+ 4^A001511(n)*x^n/n +...
		

Crossrefs

Cf. A162581, A180591, A001511.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n,4^valuation(2*m,2)*x^m/m)+x*O(x^n)),n)}
for(n=0,31,print1(a(n),", "))

Formula

Self-convolution of A162581.