login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198785 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x^n) / A(-x^n) * x^n/n ). 0
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 (list; graph; refs; listen; history; text; internal format)
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 A052974 A230585

Adjacent sequences:  A198782 A198783 A198784 * A198786 A198787 A198788

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 29 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 07:50 EST 2014. Contains 252297 sequences.