A069741 Let M_n be the n X n matrix M_(i,j)=1/(2^i+2^j), then a(n) is the numerator of det(M_n).

1, 1, 1, 49, 2401, 113060689, 260871824431729, 9708455965188246321478801, 361304320362377236050632364626862769, 3511057522394397982450601057907077808699210592028881

Offset: 1

Author

Benoit Cloitre, Apr 21 2002

Keywords

• easy
• nonn

Comments

a(n) seems always to be a square and 7 seems to follow a rule in a(n) factorization. Maximal k such that 7^k divides a(n) are 0, 0, 0, 2, 4, 6, 10, 14, 18, 24, 30, 36, 44, 52, 60, 70, 80, 90, 102, 114, 126, 142, 158, 174, 192... Hence if b(n)=maximum exponent of 7 in factorization of a(n), b(3n+1)=A049450(n); b(3n+2)=A049450(n)+2*n; b(3n+3)=A049450(n)+4n

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A069743.

Programs

PARI

for(n=1,70,print1(numerator(matdet(matrix(n,n,i,j,1/(2^i+2^j)))),","))