|
Search: id:A115142
|
|
| |
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
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: A112367 A035623 A083857 this_sequence A048963 A119458 A106356
Adjacent sequences: A115139 A115140 A115141 this_sequence A115143 A115144 A115145
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006
|
|
|
Search completed in 0.002 seconds
|
