A067550 a(n) = (n-1)!(n+2)!/(3*2^n).
1, 2, 10, 90, 1260, 25200, 680400, 23814000, 1047816000, 56582064000, 3677834160000, 283193230320000, 25487390728800000, 2650688635795200000, 315431947659628800000, 42583312934049888000000, 6472663565975582976000000, 1100352806215849105920000000
Offset: 1
Keywords
Examples
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 ...
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..120
Crossrefs
Cf. A000096.
Programs
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GAP
A067550:=List([1..20],n->Factorial(n-1)*Factorial(n+2)/(3*2^n)); # Muniru A Asiru, Mar 05 2018
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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
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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 *) -
PARI
a(n) = (n-1)!*(n+2)!/(3*2^n); \\ Altug Alkan, Mar 05 2018
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)
Extensions
a(18) from Muniru A Asiru, Mar 05 2018
Comments