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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158119 Unsigned bisection of A157308 and A157310. 4
1, 1, 3, 38, 947, 37394, 2120190, 162980012, 16330173251, 2070201641498, 324240251016266, 61525045423103316, 13913915097436287598, 3698477457114061621492, 1141824214469896983332508 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n) for n=0..50

M. Bozejko and T. Hasebe, On free infinite divisibility for classical Meixner distributions, arXiv preprint arXiv:1302.4885, 2013

FORMULA

Conjecture: a(m) == 1 (mod 2) iff m is a power of 2 or m=0. [From Paul D. Hanna, Mar 16 2009]

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 38*x^3 + 947*x^4 + 37394*x^5 +...

RELATED FUNCTIONS.

G.f. of A157308, B(x) = x + A(-x^2), satisfies the condition

that both B(x) and F(x) = B(x*F(x)) = o.g.f. of A155585

have zeros for every other coefficient after initial terms:

A157308 = [1,1,-1,0,3,0,-38,0,947,0,-37394,0,2120190,0,...];

A155585 = [1,1,0,-2,0,16,0,-272,0,7936,0,-353792,0,...].

...

G.f. of A157310, C(x) = 2+x - A(-x^2), satisfies the condition

that both C(x) and G(x) = C(x/G(x)) = o.g.f. of A157309

have zeros for every other coefficient after initial terms:

A157310 = [1,1,1,0,-3,0,38,0,-947,0,37394,0,-2120190,0,...];

A157309 = [1,1,0,-1,0,9,0,-176,0,5693,0,-272185,0,...].

...

PROG

(PARI) {a(n)=local(A=[1, 1]); for(i=1, 2*n, if(#A%2==0, A=concat(A, 0); ); if(#A%2==1, A=concat(A, t); A[ #A]=-subst(Vec(x/serreverse(x*Ser(A)))[ #A], t, 0))); (-1)^n*Vec(x/serreverse(x*Ser(A)))[2*n+1]}

CROSSREFS

Cf. A157308, A157310, A155585, A157309, A158120.

Sequence in context: A228697 A072331 A109518 * A263332 A062155 A278927

Adjacent sequences:  A158116 A158117 A158118 * A158120 A158121 A158122

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 12 2009

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.