A098107 Sum of all matrix elements M(i,j) = n!*(i/j), (i,j = 1..n).

1, 9, 66, 500, 4110, 37044, 365904, 3945024, 46195920, 584575200, 7955893440, 115942544640, 1802051072640, 29763892972800, 520699560192000, 9619862405529600, 187181055358617600, 3826464958007193600

Offset

1,2

Links

Table of n, a(n) for n=1..18.

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

Cf. A000217, A001008, A002805, A000254.

Sequence in context: A014830 A048439 A134432 * A226201 A091647 A321945

Adjacent sequences: A098104 A098105 A098106 * A098108 A098109 A098110

Keyword

nonn

Author

Alexander Adamchuk, Oct 24 2004

Status

approved