

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^(j1), 1 <= i <= n, 1 <= j <= n.


0



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

1,2


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..n1} k! = A000178(n1) (Superfactorials).


LINKS



FORMULA

a(n) = Sum_{i=1..n, j=1..n} i^(j1).
a(n) = n + Sum_{i=2..n} (i^n1)/(i1).


MATHEMATICA

Table[ n + Sum[ (i^n1)/(i1), {i, 2, n} ], {n, 1, 25} ]


CROSSREFS

Cf. A060946 = Trace of Vandermonde matrix of numbers 1, 2, ..., n.
Cf. A000178 = Superfactorials: product of first n factorials.


KEYWORD

nonn


AUTHOR



STATUS

approved



