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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A255926 Expansion of exp( Sum_{n >= 1} A210676(n)*x^n/n ). 5
1, -3, 30, -802, 45414, -4508190, 692197470, -151610017950, 44827810930305, -17193060505570335, 8298004578522898140, -4920774627129981351120, 3516683319021255757053900, -2980761698101283167670391780, 2956463734237276273792194346560, -3392220222832838757465019626175680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It appears that this sequence is integer valued.

The o.g.f. A(x) = 1 - 3*x + 30*x^2 - 802*x^3 + ... for this sequence is such that 1 + x*d/dx( log(A(x) ) is the o.g.f. for A210676.

This sequence is the particular case m = -3 of the following general conjecture.

Let m be an integer and consider the sequence u(n) defined by the recurrence u(n) = m*Sum_{k = 0..n-1} binomial(2*n,2*k)*u(k) with the initial condition u(0) = 1. Then the expansion of exp( Sum_{n >= 1} u(n)*x^n/n ) ) has integer coefficients.

For cases see A255882(m = -2), A255881(m = -1), A255928(m = 1), A255929(m = 2) and A255930(m = 3).

Note that u(n), as a polynomial in the variable m, is the n-th row polynomial of A241171.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

O.g.f.: exp(-3*x + 51*x^2/2 - 2163*x^3/3 + 171231*x^4/4 + ...) = 1 - 3*x + 30*x^2 - 802*x^3 + 45414*x^4 - ....

a(0) = 1 and a(n) = 1/n*Sum_{k = 0..n-1} A210676(n-k)*a(k) for n >= 1.

MAPLE

#A255926

A210676 := proc (n) option remember; if n = 0 then 1 else -3*add(binomial(2*n, 2*k)*A210676(k), k = 0 .. n-1) end if; end proc:

A255926 := proc (n) option remember; if n = 0 then 1 else add(A210676(n-k)*A255926(k), k = 0 .. n-1)/n end if; end proc:

seq(A255926(n), n = 0 .. 16);

CROSSREFS

Cf. A210676, A241171, A255882(m = -2), A255881(m = -1), A255928(m = 1), A255929(m = 2), A255930(m = 3).

Sequence in context: A082879 A012007 A065753 * A113677 A306092 A174549

Adjacent sequences:  A255923 A255924 A255925 * A255927 A255928 A255929

KEYWORD

sign,easy

AUTHOR

Peter Bala, Mar 11 2015

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 April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)