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
Muniru A Asiru, Table of n, a(n) for n = 1..120
FORMULA
a(n+1)/a(n) = A000096(n) = n(n+3)/2. - Alexander Adamchuk, May 20 2006
From Amiram Eldar, Feb 02 2023: (Start)
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} ]
Table[(n-1)!(n+2)!/3/2^n, {n, 1, 20}] (* Alexander Adamchuk, May 20 2006 *)
PROG
(GAP) A067550:=List([1..20], n->Factorial(n-1)*Factorial(n+2)/(3*2^n)); # Muniru A Asiru, Mar 05 2018
(PARI) a(n) = (n-1)!*(n+2)!/(3*2^n); \\ Altug Alkan, Mar 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jan 28 2002
EXTENSIONS
a(18) from Muniru A Asiru, Mar 05 2018
STATUS
approved