|
Search: id:A115147
|
|
| |
|
| 1, -8, 20, -16, 2, 0, 0, 0, -1, -8, -44, -208, -910, -3808, -15504, -62016, -245157, -961400, -3749460, -14567280, -56448210, -218349120, -843621600, -3257112960, -12570420330, -48507033744, -187187399448, -722477682080, -2789279908316, -10772391370048
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
O.g.f.: 1/c(x)^8 = P(9, x) - x*P(8, 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(9, x)= 1-7*x+15*x^2-10*x^3+x^4 and P(8, x)=1-6*x+10*x^2-4*x^3.
a(n)=-C8(n-8), n>=8, with C8(n):=A003518(n+3) (eighth convolution of Catalan numbers). a(0)=1, a(1)=-8, a(2)=30, a(3)=-16, a(4)=2, a(5)=a(6)=a(7)=0. [1, -8, 20, -16, 2] is row n=8 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.
|
|
CROSSREFS
|
Cf. A115146 (seventh convolution).
Sequence in context: A120081 A081963 A128909 this_sequence A022700 A100212 A083094
Adjacent sequences: A115144 A115145 A115146 this_sequence A115148 A115149 A115150
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006
|
|
|
Search completed in 0.002 seconds
|
