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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A289085 Imaginary parts of the recursive sequence a(n+2) = Sum_{k=0..n} binomial(n,k)a(k)a(n+1-k), with a(0)=2, a(1)=i. 8
0, 1, 2, 4, 8, 12, -36, -656, -6016, -45712, -303584, -1614784, -3151424, 89449152, 2020752864, 30106674944, 371094759424, 3803441275648, 27086999353856, -53440551394304, -7360216885479424, -195653223115035648, -3852848368364645376, -62648371228429684736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here, i is the imaginary unit. The complex integer sequence c(n) = A289084(n) + i*A289085(n) is one of a family of sequences whose e.g.f.s satisfy the differential equation f''(z) = f'(z)f(z). For more details, see A289064 and A289082.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..200

S. Sykora, Sequences related to the differential equation f'' = af'f, Stan's Library, Vol. VI, Jun 2017.

FORMULA

E.g.f.: imag(2*L0*tan(L0*z + L1)), where L0 = sqrt(i/2-1) and L1 = acos(sqrt(1+2*i)).

MATHEMATICA

a[0]=2; a[1]=I; a[n_]:=a[n]=Sum[Binomial[n - 2, k] a[k] a[n - 1 - k], {k, 0, n - 2}]; Im[Table[a[n], {n, 0, 50}]] (* Indranil Ghosh, Jul 20 2017 *)

PROG

(PARI) c0=2; c1=I; nmax = 200;

  a=vector(nmax+1); a[1]=c0; a[2]=c1;

  for(m=0, #a-3, a[m+3]=sum(k=0, m, binomial(m, k)*a[k+1]*a[m+2-k]));

  imag(a)

CROSSREFS

Cf. A289084 (real part).

Sequences for other starting pairs: A000111 (1,1), A289064 (1,-1), A289065 (2,-1), A289066 (3,1), A289067 (3,-1), A289068 (1,-2), A289069 (3,-2), A289070 (0,3), A289082 and A289083 (1,i), A289086 and A289087 (1,2i), A289088 and A289089 (2,2i).

Sequence in context: A202148 A215825 A177268 * A242924 A133802 A076202

Adjacent sequences:  A289082 A289083 A289084 * A289086 A289087 A289088

KEYWORD

sign

AUTHOR

Stanislav Sykora, Jul 19 2017

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 September 26 10:52 EDT 2017. Contains 292518 sequences.