The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282876 Expansion of ((1 + 4*x + 8*x^2)^(3/2) - (1 + 6*x + 18*x^2 + 20*x^3)) / (2*x^4) in powers of x. 0
3, -6, 10, -12, 3, 34, -114, 204, -114, -636, 2676, -5528, 3939, 17778, -83994, 186972, -150438, -609524, 3091020, -7204008, 6237902, 23649204, -125807412, 302476536, -275144388, -996903096, 5489607272, -13498689840, 12721569699, 44596212754, -252074322858 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Ewan Delanoy, Divisibility property for sequence a(n+2) = -2(n-1)(n+3)a(n) - (2n+3)a(n+1), Mathematics Stack Exchange question 2728009, Apr 08 2018.
FORMULA
0 = (8*n + 8)*a(n) + (4*n + 14)*a(n+1) + (n + 6)*a(n+2) for all n in Z if a(-1)=10, a(-2)=9, a(-3)=3, a(-4)=1/2, and also
0 = a(n)*(+64*a(n+1) +112*a(n+2) +48*a(n+3)) +a(n+1)*(-48*a(n+1) -16*a(n+2) +14*a(n+3)) +a(n+2)*(-6*a(n+2) +a(n+3)) for all n in Z.
D-finite with recurrence (n+4)*a(n) +2*(2*n+3)*a(n-1) +8*(n-1)*a(n-2)=0. - R. J. Mathar, Sep 24 2021
EXAMPLE
G.f. = 3 - 6*x + 10*x^2 - 12*x^3 + 3*x^4 + 34*x^5 - 114*x^6 + 204*x^7 + ...
MATHEMATICA
a[ n_] := If[ n < 1, 3 Boole[n==0], Sum[ (-1)^k Binomial[k, 2 k - n - 4] (2 k - 5)! / (2^(k - 3) k! (k - 3)!), {k, 3, n + 4}] 24 2^n];
PROG
(PARI) {a(n) = if( n<1, 3*(n==0), sum(k=3, n+4, (-1)^k * binomial(k, 2*k-n-4) * (2*k-5)! / (2^(k-3) * k! * (k-3)!)) * 24 * 2^n)};
CROSSREFS
Sequence in context: A351827 A351828 A158975 * A363775 A261662 A345915
KEYWORD
sign
AUTHOR
Michael Somos, Oct 26 2018
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 00:18 EDT 2024. Contains 373362 sequences. (Running on oeis4.)