|
|
A067550
|
|
a(n) = (n-1)!(n+2)!/(3*2^n).
|
|
12
|
|
|
1, 2, 10, 90, 1260, 25200, 680400, 23814000, 1047816000, 56582064000, 3677834160000, 283193230320000, 25487390728800000, 2650688635795200000, 315431947659628800000, 42583312934049888000000, 6472663565975582976000000, 1100352806215849105920000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Determinant of n X n matrix whose diagonal are the first n triangular numbers and all other elements are 1's.
|
|
LINKS
|
|
|
FORMULA
|
Sum_{n>=1} 1/a(n) = 3*BesselI(3, 2*sqrt(2))/sqrt(2).
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*BesselJ(3, 2*sqrt(2))/sqrt(2). (End)
|
|
EXAMPLE
|
The determinant begins:
1 1 1 1 1 1 1 ...
1 3 1 1 1 1 1 ...
1 1 6 1 1 1 1 ...
1 1 1 10 1 1 1 ...
1 1 1 1 15 1 1 ...
1 1 1 1 1 21 1 ...
|
|
MAPLE
|
d:=(i, j)->`if`(i<>j, 1, i*(i+1)/2):
seq(LinearAlgebra[Determinant](Matrix(n, d)), n=1..20); # Muniru A Asiru, Mar 05 2018
|
|
MATHEMATICA
|
Table[ Det[ DiagonalMatrix[ Table[ i(i + 1)/2 - 1, {i, 1, n} ] ] + 1 ], {n, 1, 20} ]
|
|
PROG
|
(PARI) a(n) = (n-1)!*(n+2)!/(3*2^n); \\ Altug Alkan, Mar 05 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|