login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211896 G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^4 * x^n/n ), where Jacobsthal(n) = A001045(n). 4
1, 3, 6, 90, 723, 10689, 130428, 1862580, 25594611, 368313993, 5289203262, 77279744418, 1134460916361, 16798605635235, 249994099311288, 3740771822960664, 56208829313956998, 847934859174601650, 12834366187138678836, 194855374723972622988, 2966358133685609559042 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Given g.f. A(x), note that A(x)^(1/3) is not an integer series.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: ( (1+2*x)^4*(1+8*x)^4 / ((1-x)*(1-4*x)^6*(1-16*x)) )^(1/27).

G.f.: exp( Sum_{n>=1} (2^n - (-1)^n)^4 / 27 * x^n/n ).

EXAMPLE

G.f.: A(x) = 1 + 3*x + 6*x^2 + 90*x^3 + 723*x^4 + 10689*x^5 + 130428*x^6 +...

such that

log(A(x))/3 = x + x^2/2 + 3^4*x^3/3 + 5^4*x^4/4 + 11^4*x^5/5 + 21^4*x^6/6 + 43^4*x^7/7 +...+ Jacobsthal(n)^4*x^n/n +...

Jacobsthal numbers begin:

A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,...].

PROG

(PARI) {Jacobsthal(n)=polcoeff(x/(1-x-2*x^2+x*O(x^n)), n)}

{a(n)=polcoeff(exp(sum(k=1, n, 3*Jacobsthal(k)^4*x^k/k)+x*O(x^n)), n)}

for(n=0, 30, print1(a(n), ", "))

(PARI) {a(n)=polcoeff(((1+2*x)^4*(1+8*x)^4/((1-x)*(1-4*x)^6*(1-16*x))+x*O(x^n))^(1/27), n)}

CROSSREFS

Cf. A211893, A211894, A211895, A207969, A001045 (Jacobsthal).

Sequence in context: A213138 A331403 A157197 * A299433 A036286 A084008

Adjacent sequences:  A211893 A211894 A211895 * A211897 A211898 A211899

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 25 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 13:55 EST 2020. Contains 331010 sequences. (Running on oeis4.)