A161803 G.f.: A(x) = exp( Sum_{n>=1} A162552(n) * 2*A006519(n) * x^n/n ).

1, 2, 0, -2, 6, 12, 0, -8, 24, 44, 0, -30, 54, 104, 0, -60, 238, 466, 0, -402, 924, 1892, 0, -1228, 3264, 6006, 0, -4052, 6688, 13052, 0, -7452, 16536, 32140, 0, -24828, 39660, 85744, 0, -53592, 114336, 212406, 0, -141090, 190754, 386956, 0, -216572, 136078

Offset

0,2

Comments

A162552 forms the l.g.f. of log[ Sum_{n>=0} x^(n^2) ], while

2*A006519 forms the l.g.f. of binary partitions (A000123) and

A006519(n) is the highest power of 2 dividing n.

Links

Table of n, a(n) for n=0..48.

Example

G.f.: 1 + 2*x - 2*x^3 + 6*x^4 + 12*x^5 - 8*x^7 + 24*x^8 + 44*x^9 +...

Prog

(PARI) {a(n)=local(SQ=sum(m=0, sqrtint(n+1), x^(m^2))+x*O(x^n), L=sum(m=1, n, 2*2^valuation(m, 2)*polcoeff(log(SQ), m)*x^m)+x*O(x^n)); polcoeff(exp(L), n)}

Crossrefs

Cf. A161800, A162552.

Sequence in context: A303439 A303345 A175802 * A057980 A242840 A081081

Adjacent sequences: A161800 A161801 A161802 * A161804 A161805 A161806

Keyword

sign

Author

Paul D. Hanna, Jul 19 2009

Status

approved