1,2

a(n) is the number of n X n matrices with nonnegative integer entries such that every row sum equals 2. - Sharon Sela (sharonsela(AT)hotmail.com), May 08 2002

Resultant of the polynomials P(n,x) and Q(n,x) where P(n,x)=sum(k=1,n,k*(-x)^k) and Q(n,x)=x^n-1. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003

a(n) is also the number of positive-volume, axis-aligned, n-dimensional rectangular solids that have vertices in the set {0,1,...,n}^n. Proof: If (M_1,...,M_n) is the corner with the maximum coordinate values for such a solid, then there are (M_1)*...*(M_n) possibilities for the corner with the minimum coordinate values. The sum over all possibilities for M_1, ..., M_n can be factored into the product of n sums; each of the n sums simplifies to n(n+1)/2. [From Lee A. Newberg (integer(AT)quantconsulting.com), Aug 31 2009]

Harry J. Smith, Table of n, a(n) for n=1,...,100

Sum(i:1,n,j:1,n,k:1,n...(i*j*k*...)). E.g. a(2)= 9 because 1*1 + 1*2 + 2*1 + 2*2 = 9 - Ben Thurston (benthurston27(AT)yahoo.com), Aug 15 2006

a:=n->mul(sum(j, j=0..n), k=1..n): seq(a(n), n=1..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007

a:=n->mul(binomial(n+2, 2), k=0..n): seq(a(n), n=0..12); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 02 2007

(C++) e.g. n = 6 int sum = 0; for(int i = 1; i < 7; i++) { for(int j = 1; j < 7; j++) { for(int k=1; k<7; k++) { for(int l = 1; l < 7; l++) { for(int m = 1; m < 7; m++) { for(int n = 1; n < 7; n++) { sum += i*j*k*l*m*n; } } } } } } cout << sum << endl; system("pause"); - Ben Thurston (benthurston27(AT)yahoo.com), Aug 15 2006

(PARI) { for (n=1, 100, write("b061718.txt", n, " ", (n*(n + 1)/2)^n) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 26 2009]

Cf. A066300.

Sequence in context: A007107 A064633 A084942 this_sequence A085741 A152288 A157692

Adjacent sequences: A061715 A061716 A061717 this_sequence A061719 A061720 A061721

easy,nonn

Jason Earls (zevi_35711(AT)yahoo.com), Jun 20 2001