A262825 G.f.: exp( Sum_{n>=1} x^n/n * 3^(n^2)/(1 + 3^(n^2)*x^n) ).

1, 3, 36, 6687, 10778724, 169490235888, 25016281203451185, 34185693515006540036988, 429210580094320740939492003864, 49269611092414637899756996954236224964, 51537752221009977969797967261567868189156062717, 490093718313094497196906721743434604298698182091562669412, 42294065506171581216310316433524563489152717911911865589940031127588

Offset

0,2

Comments

Compare to g.f. of A010054:

exp( Sum_{n>=1} x^n/(1 + x^n)/n ) = 1 + x + x^3 + x^6 + x^10 +...

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} -(-1)^d * 3^(n^2/d) * d ).

Example

 G.f.: A(x) = 1 + 3*x + 36*x^2 + 6687*x^3 + 10778724*x^4 + 169490235888*x^5 +...
where
log(A(x)) = 3*x/(1 + 3*x) + 3^4/(1 + 3^4*x^2)*x^2/2 + 3^9/(1 + 3^9*x^3)*x^3/3 + 3^16/(1 + 3^16*x^4)*x^4/4 + 3^25/(1 + 3^25*x^5)*x^5/5 +...
Explicitly,
log(A(x)) = 3*x + 63*x^2/2 + 19764*x^3/3 + 43033275*x^4/4 + 847288610658*x^5/5 + 150094634523748092*x^6/6 +  + 239299329230617529605392*x^7/7 +...

Prog

 (PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(k=1, n, x^k/k * 3^(k^2)/(1 + 3^(k^2)*x^k +x*O(x^n)))), n))}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = polcoeff( exp( sum(m=1, n, x^m/m * sumdiv(m, d, -(-1)^d * 3^(m^2/d) * d) ) +x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A158096.

Sequence in context: A325907 A158093 A163966 * A088322 A342300 A080807

Adjacent sequences: A262822 A262823 A262824 * A262826 A262827 A262828

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2015

Status

approved