A195462 1!*2!*3!*...*n!*H(n); H(n) the n-th harmonic number.

1, 3, 22, 600, 78912, 60963840, 325173657600, 13743074967552000, 5190968541142056960000, 19502847300506769948672000000, 802654006697267902579055001600000000, 395082050396018659026474786525020160000000000

Offset

1,2

Comments

Determinant of the n x n - Matrix A[i,j] with A[1,j]=1 (1<=j<=n) and A[i,j]=j^i (i>1, 1<=j<=n) [L. Theisinger].

References

L. Theisinger, Bemerkung über die harmonische Reihe. Monatshefte für Mathematik und Physik XXVI. Jahrgang (1915), 132-134.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..30

Formula

a(n) = A000178(n)*A001008(n)/A002805(n).

Example

a(4) = 1!*2!*3!*4!*H(4) = 1*2*6*24*(25/12) = 600.

Maple

a:= n-> mul(j^(n-j+1), j=2..n) * add(1/k, k=1..n):
seq(a(n), n=1..15);  # Alois P. Heinz, Sep 21 2011

Crossrefs

Cf. A000178, A001008, A002805.

Sequence in context: A272659 A233748 A153230 * A276749 A232016 A365116

Adjacent sequences: A195459 A195460 A195461 * A195463 A195464 A195465

Keyword

nonn,easy

Author

Franz Vrabec, Sep 21 2011

Status

approved