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A115142 Third convolution of A115140. 3
1, -3, 0, -1, -3, -9, -28, -90, -297, -1001, -3432, -11934, -41990, -149226, -534888, -1931540, -7020405, -25662825, -94287120, -347993910, -1289624490, -4796857230, -17902146600, -67016296620, -251577050010, -946844533674, -3572042254128, -13505406670700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1668

FORMULA

O.g.f.: 1/c(x)^3 = P(4, x) - x*P(3, 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(4, x)=1-2*x and P(3, x)=1-x.

a(n)=-C3(n-3), n>=3, with C3(n):= A000245(n+1) (third convolution of Catalan numbers). a(0)=1, a(1)=-3, a(2)=0. [1, -3] is the row n=3 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.

CROSSREFS

Cf. A115141 (second convolution).

Sequence in context: A035623 A248949 A083857 * A273083 A247629 A178116

Adjacent sequences:  A115139 A115140 A115141 * A115143 A115144 A115145

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Jan 13 2006

STATUS

approved

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Last modified February 18 15:33 EST 2018. Contains 299324 sequences. (Running on oeis4.)