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A098107
Sum of all matrix elements M(i,j) = n!*(i/j), (i,j = 1..n).
0
1, 9, 66, 500, 4110, 37044, 365904, 3945024, 46195920, 584575200, 7955893440, 115942544640, 1802051072640, 29763892972800, 520699560192000, 9619862405529600, 187181055358617600, 3826464958007193600
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