|
|
A130031
|
|
Row sums of triangle A129467.
|
|
5
|
|
|
1, 1, -1, 5, -55, 1045, -30305, 1242505, -68337775, 4851982025, -431826400225, 47069077624525, -6166049168812775, 955737621165980125, -172988509431042402625, 36154598471087862148625, -8640949034589999053521375, 2341697188373889743504292625
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
See the M. Bruschi et al. reference given in A129467.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{j=0..n} A129467(n,j), n >= 0.
a(n) = Sum_{j=0..n-1} A130559(n, j), n>= 1.
a(n) = (-1)^n*Product_{k=1..n} (k^2 - k - 1).
a(n) ~ 2*(-1)^n * cos(sqrt(5)*Pi/2) * n^(2*n) / exp(2*n). (End)
|
|
MATHEMATICA
|
Table[(-1)^n*Product[k^2-k-1, {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 24 2016 *)
Table[FullSimplify[(-1)^n * Cos[Sqrt[5]*Pi/2] * Gamma[n+(Sqrt[5]+1)/2] * Gamma[n-(Sqrt[5]-1)/2]/Pi], {n, 0, 20}] (* Vaclav Kotesovec, Aug 24 2016 *)
|
|
PROG
|
(Magma) [1] cat [n le 1 select 1 else -(n^2-n-1)*Self(n-1): n in [1..30]]; // G. C. Greubel, Feb 10 2024
(SageMath)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|