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A115149 Tenth convolution of A115140. 10
1, -10, 35, -50, 25, -2, 0, 0, 0, 0, -1, -10, -65, -350, -1700, -7752, -33915, -144210, -600875, -2466750, -10015005, -40320150, -161280600, -641886000, -2544619500, -10056336264, -39645171810, -155989499540, -612815891050, -2404551645100, -9425842448792 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Because (x*c(x))^n + (1/c(x))^n = L(n,-x)= sum(A034807(n,k)*(-x)^k,k=0..floor(n/2)) the sequence starts with the Lucas polynomial L(10,-x) (of degree 5).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1671

FORMULA

O.g.f.: 1/c(x)^10 = P(11, x) - x*P(10, 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(11, x)=1-9*x+28*x^2-35*x^3+15*x^4-x^5 and P(10, x)=1-8*x+21*x^2-20*x^3+5*x^4.

a(n)=-C10(n-10), n>=10, with C10(n):= (n+4) (eighth convolution of Catalan numbers). a(0)=1, a(1)=-10, a(2)=35, a(3)=-50, a(4)=25, a(5)=-2, a(6)=a(7)=a(8)=a(9)=0. [1, -10, 35, -50, 25, -2] is row n=10 of signed A034807 (signed Lucas polynomials).

CROSSREFS

Cf. A115148 (ninth convolution).

Sequence in context: A010818 A243939 A065195 * A044087 A022702 A044468

Adjacent sequences:  A115146 A115147 A115148 * A115150 A115151 A115152

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

STATUS

approved

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Last modified February 17 18:28 EST 2018. Contains 299296 sequences. (Running on oeis4.)