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A115143 a(n) = -4*binomial(2*n-5, n-4)/n for n>0 and a(0) = 1. 2
1, -4, 2, 0, -1, -4, -14, -48, -165, -572, -2002, -7072, -25194, -90440, -326876, -1188640, -4345965, -15967980, -58929450, -218349120, -811985790, -3029594040, -11338026180, -42550029600, -160094486370, -603784920024, -2282138106804, -8643460269248, -32798844771700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Previous name: Fourth convolution of A115140.

a(n+4) := - convolution ( A000108(n+1) ), n=0,1,... - Tilman Neumann, Jan 05 2009

Self-convolution of A115141. - R. J. Mathar, Sep 26 2012

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1669

FORMULA

O.g.f.: 1/c(x)^4 = P(5, x) - x*P(4, x)*c(x) with the o.g.f. c(x) := (1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers) and the polynomials P(n, x) defined in A115139. Here P(5, x) = 1-5*x+6*x^2-x^3 and P(4, x) = 1-2*x.

a(n) = -C4(n-4), n>=4, with C4(n) := A002057(n) (fourth convolution of Catalan numbers). a(0)=1, a(1)=-4, a(2)=2, a(3)=0. [1, -4, 2] is row n=4 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.

E.g.f.: 1 - 3*x + 1/2*x^2 - x*Q(0), where Q(k)= 1 - 2*x/(k+2 - (k+2)*(2*k+1)/(2*k+1 - (k+2)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Apr 28 2013

MAPLE

A115143 := n -> `if`(n=0, 1, -4*binomial(2*n-5, n-4)/n):

seq(A115143(n), n=0..28); # Peter Luschny, Feb 27 2017

MATHEMATICA

Join[{1}, Table[-4*Binomial[2n-5, n-4]/n, {n, 30}]] (* Harvey P. Dale, Dec 01 2017 *)

CROSSREFS

Cf. A115140, A115141, A115142 (third convolution), A099376, A000108.

Sequence in context: A137986 A093486 A259618 * A093556 A021242 A088393

Adjacent sequences:  A115140 A115141 A115142 * A115144 A115145 A115146

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

EXTENSIONS

Simpler name from Peter Luschny, Feb 27 2017

STATUS

approved

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Last modified October 15 10:55 EDT 2018. Contains 316222 sequences. (Running on oeis4.)