A198785 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x^n) / A(-x^n) * x^n/n ).

1, 1, 3, 5, 14, 28, 77, 173, 485, 1165, 3335, 8341, 24331, 62455, 184783, 483127, 1445429, 3830911, 11562247, 30969809, 94134108, 254285698, 777410651, 2114690863, 6496549393, 17774924057, 54831676621, 150766702399, 466729836290, 1288810006264, 4002059363580

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

Euler transform of the coefficients in A(x)/A(-x), where A(x) is the g.f. of this sequence.

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 5*x^3 + 14*x^4 + 28*x^5 + 77*x^6 + 173*x^7 +...
where
log(A(x)) = A(x)/A(-x)*x + A(x^2)/A(-x^2)*x^2/2 + A(x^3)/A(-x^3)*x^3/3 +...
more explicitly,
log(A(x)) = x + 5*x^2/2 + 7*x^3/3 + 29*x^4/4 + 51*x^5/5 + 191*x^6/6 + 407*x^7/7 + 1485*x^8/8 + 3409*x^9/9 + 12315*x^10/10 +...
This sequence equals the Euler transform of coefficients in A(x)/A(-x):
[1,2,2,6,10,30,58,182,378,1226,2658,8798,19634,65990,150338,511054,...];
A(x) = 1/((1-x) *(1-x^2)^2 *(1-x^3)^2 *(1-x^4)^6 *(1-x^5)^10 *(1-x^6)^30 *(1-x^7)^58 *(1-x^8)^182 *(1-x^9)^378 *...).

Prog

 (PARI) {a(n)=local(A=1+x, B); for(i=1, n, B=(A/subst(A, x, -x)); A=exp(sum(m=1, n, subst(B, x, x^m+x*O(x^n))*x^m/m))); polcoeff(A, n)}

Crossrefs

Sequence in context: A145974 A147544 A192478 * A222380 A271867 A295064

Adjacent sequences: A198782 A198783 A198784 * A198786 A198787 A198788

Keyword

nonn

Author

Paul D. Hanna, Oct 29 2011

Status

approved