0,3

a(n)=(-1)^n/det(M_n) where M_n is the n X n matrix m(i,j)=(-1)^i/i^j - Benoit Cloitre (benoit7848c(AT)orange.fr), May 28 2002

a(n) = determinant of the n X n matrix M(n) where m(i,j)=B(n,i,j) and B(n,i,x) denote the Bernstein polynomial : B(n,i,x)=binomial(n,i)*(1-x)^(n-i)*x^i. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Azarian, Mohammad K., On the hyperfactorial function, hypertriangular function and the discriminants of certain polynomials. Int. J. Pure Appl. Math. 36 (2007), 251-257.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 135-145.

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 50.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 477.

N. J. A. Sloane, Table of n, a(n) for n = 1..36

S. R. Finch, Glaisher-Kinkelin Constant (gives asymptotic expressions for A002109, A000178) [At present this link does not work]

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to factorial numbers

Determinant of n X n matrix m(i, j)=binomial(i*j, i) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 27 2003

f := proc(n) local k; mul(k^k, k=1..n); end;

a[0]:=1:for n from 1 to 20 do a[n]:=product(n!/k!, k=0..n) od: seq(a[n], n=0..11); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2007

seq(mul(mul(k, j=1..k), k=1..n), n=0..11); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007

lst={}; s=1; Do[AppendTo[lst, s*=n^n], {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]

Table[Hyperfactorial[n], {n, 0, 11}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]

Cf. A000178, A000142.

A002109(n)*A000178(n-1) = (n!)^n = A036740(n) for n >= 1.

Cf. A001358, A002981, A002982, A100015, A005234, A014545, A018239, A006794, A057704, A057705.

Cf. A074962 [Glaisher-Kinkelin constant, also gives an asymptotic approximation for the hyperfactorials].

Adjacent sequences: A002106 A002107 A002108 this_sequence A002110 A002111 A002112

Sequence in context: A090205 A061464 A107048 this_sequence A076265 A114876 A037980

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).