A162420 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*|A002129(n)|*x^n/n ).

1, 1, 2, 7, 16, 28, 57, 118, 238, 432, 792, 1491, 2759, 4836, 8522, 15126, 26419, 45114, 76883, 130792, 220578, 367144, 608252, 1005102, 1649904, 2684354, 4349068, 7022762, 11278628, 18002603, 28621347, 45345249, 71528789, 112295812

Offset

0,3

Comments

A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], while

A000203 forms the l.g.f. of log[ 1/eta(x) ]

where eta(x)^3 = Sum_{n>=0} (-1)^n*(2n+1)*x^(n(n+1)/2).

Links

Table of n, a(n) for n=0..33.

Formula

G.f.: A(x) = exp( L(x) ) where L(x) is the l.g.f. of A162419.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 16*x^4 + 28*x^5 + 57*x^6 +...
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 35*x^4/4 + 36*x^5/5 + 48*x^6/6 +...
where log(A(x)) is the l.g.f. of A162419 and
log(A(x)) = 1*1*x + 3*1*x^2/2 + 4*4*x^3/3 + 7*5*x^4/4 + 6*6*x^5/5 +...
is formed from the term-wise product of the (unsigned) sequences:
A000203:[1, 3,4, 7,6,12,8, 15,13,18,12, 28,14,24,24, 31,18,...];
A002129:[1,-1,4,-5,6,-4,8,-13,13,-6,12,-20,14,-8,24,-29,18,...].

Prog

(PARI) {a(n)=local(L=sum(m=1, n, sigma(m)*sumdiv(m, d, (-1)^(m-d)*d)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

Crossrefs

Cf. A162419, A000203, A002129.

Sequence in context: A070169 A293410 A348270 * A130883 A360284 A005581

Adjacent sequences: A162417 A162418 A162419 * A162421 A162422 A162423

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2009

Status

approved