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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.

%I A128884 #14 Feb 16 2025 08:33:05
%S A128884 1,5,23,144,1279,15035,219463,3816512,76928685,1762344781,45207853767,
%T A128884 1283438430208,39944988007339,1352308628695895,49471532968242991,
%U A128884 1944732944768690432,81748776383970349721,3659142661552743151353
%N 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.
%C A128884 p divides a(p+1) for odd primes p.
%C A128884 p^2 divides a(p+1) for prime p = {3, 7, 71, ...}.
%C A128884 Determinant of n X n Vandermonde matrix of numbers 1,2,...,n equals Product_{k=1..n-1} k! = A000178(n-1) (Superfactorials).
%H A128884 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VandermondeMatrix.html">Vandermonde Matrix</a>
%F A128884 a(n) = Sum_{i=1..n, j=1..n} i^(j-1).
%F A128884 a(n) = n + Sum_{i=2..n} (i^n-1)/(i-1).
%t A128884 Table[ n + Sum[ (i^n-1)/(i-1), {i,2,n} ], {n,1,25} ]
%Y A128884 Cf. A060946 = Trace of Vandermonde matrix of numbers 1, 2, ..., n.
%Y A128884 Cf. A000178 = Superfactorials: product of first n factorials.
%K A128884 nonn
%O A128884 1,2
%A A128884 _Alexander Adamchuk_, Apr 18 2007