OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Triangular Number.
Eric Weisstein's World of Mathematics, Harmonic Number.
Eric Weisstein's World of Mathematics, Stirling Number of the First Kind.
FORMULA
a(n) = n!*Sum[Sum[(i/j), {i, 1, n}], {j, 1, n}].
From Alexander Adamchuk, Nov 09 2004: (Start)
a(n) = (-1)^(n+1)*(n*(n+1)/2)*Stirling1(n+1, 2).
E.g.f.: x*(x+2-2*log(1-x))/(2*(1-x)^3). (End)
a(n) = n! * T(n) * H(n), where T(n) = n(n+1)/2 is triangular number A000217(n) and H(n) = Sum(1/i) (i=1..n) is harmonic number A001008(n)/A002805(n). - Alexander Adamchuk, Nov 09 2004
E.g.f.: (1+4*x+(1/2)*x^2-(2*x+1)*log(1-x))/(x-1)^4. - Mark van Hoeij, Nov 09 2011
EXAMPLE
a(2) = 2! * (1/1 + 2/1 + 1/2 + 2/2) = 9.
MATHEMATICA
Table[n!*Sum[Sum[(i/j), {i, 1, n}], {j, 1, n}], {n, 1, 20}]
PROG
(PARI) a(n) = n!*sum(i=1, n, sum(j=1, n, i/j)); \\ Michel Marcus, May 11 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Oct 24 2004
STATUS
approved