A128884 Sum of all matrix elements of n X n Vandermonde matrix of numbers 1,2,...,n, i.e., the matrix A with A[i,j] = i^(j-1), 1 <= i <= n, 1 <= j <= n.

1, 5, 23, 144, 1279, 15035, 219463, 3816512, 76928685, 1762344781, 45207853767, 1283438430208, 39944988007339, 1352308628695895, 49471532968242991, 1944732944768690432, 81748776383970349721, 3659142661552743151353

Offset: 1

Author

Alexander Adamchuk, Apr 18 2007

Keywords

• nonn

Comments

p divides a(p+1) for odd primes p.

p^2 divides a(p+1) for prime p = {3, 7, 71, ...}.

Determinant of n X n Vandermonde matrix of numbers 1,2,...,n equals Product_{k=1..n-1} k! = A000178(n-1) (Superfactorials).

Links

• Eric Weisstein's World of Mathematics, Vandermonde Matrix

Crossrefs

Cf. A060946 = Trace of Vandermonde matrix of numbers 1, 2, ..., n.

Cf. A000178 = Superfactorials: product of first n factorials.

Programs

Mathematica

Table[ n + Sum[ (i^n-1)/(i-1), {i,2,n} ], {n,1,25} ]

Formula

a(n) = Sum_{i=1..n, j=1..n} i^(j-1).

a(n) = n + Sum_{i=2..n} (i^n-1)/(i-1).