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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091593 Reversion of Jacobsthal numbers A001045. 6
1, -1, -1, 5, -3, -21, 51, 41, -391, 407, 1927, -6227, -2507, 49347, -71109, -236079, 966129, 9519, -7408497, 13685205, 32079981, -167077221, 60639939, 1209248505, -2761755543, -4457338681, 30629783831, -22124857219, -206064020315, 572040039283, 590258340811 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Hankel transform is (-2)^C(n+1,2). - Paul Barry, Apr 28 2009

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for reversions of series

FORMULA

G.f.: (-(1+x)+sqrt(1+2*x+9*x^2))/(4*x^2). - Corrected by Seiichi Manyama, May 12 2019

a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2k)*C(k)*(-1)^(n-k)2^k, where C(n) is A000108. - Paul Barry, May 16 2005

G.f.: 1/(1+x+2x^2/(1+x+2x^2/(1+x+2x^2/(1+x+2x^2/(1+ ... (continued fraction). - Paul Barry, Apr 28 2009

a(n) = Sum_{i=0..n} (2^(i)*(-1)^(n-i)*binomial(n+1,i)^2*(n-i+1)/(i+1))/(n+1). - Vladimir Kruchinin, Oct 12 2011

Conjecture: (n+2)*a(n) +(2*n+1)*a(n-1) +9*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 26 2012

a(n) = (-1)^n*hypergeom([-n/2, (1-n)/2], [2], -8). - Peter Luschny, May 28 2014

R. J. Mathar's conjecture confirmed by Maple using this hypergeom form. - Robert Israel, Sep 22 2014

MAPLE

a := n -> hypergeom([-n, -n-1], [2], -2);

seq(round(evalf(a(n), 99)), n=0..30); # Peter Luschny, Sep 22 2014

MATHEMATICA

a[n_] := Hypergeometric2F1[-n - 1, -n - 1, 2, -2] + (n + 1)*Hypergeometric2F1[-n, -n, 3, -2]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Oct 03 2016, after Vladimir Kruchinin *)

PROG

(Maxima)

a(n):=sum(2^(i)*(-1)^(n-i)*binomial(n+1, i)^2*(n-i+1)/(i+1), i, 0, n)/(n+1); (* Vladimir Kruchinin, Oct 12 2011 *)

(Sage) # Algorithm of L. Seidel (1877)

def A091593_list(n) :

    D = [0]*(n+2); D[1] = 1

    R = []; b = false; h = 1

    for i in range(2*n) :

        if b :

            for k in range(1, h, 1) : D[k] += -2*D[k+1]

            R.append(D[1])

        else :

            for k in range(h, 0, -1) : D[k] += D[k-1]

            h += 1

        b = not b

    return R

A091593_list(30)  # Peter Luschny, Oct 19 2012

CROSSREFS

Cf. A154825.

Sequence in context: A199638 A296356 A154825 * A139699 A303634 A069607

Adjacent sequences:  A091590 A091591 A091592 * A091594 A091595 A091596

KEYWORD

easy,sign

AUTHOR

Paul Barry, Jan 23 2004

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 August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)