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A054780 Number of n-covers of a labeled n-set. 2
1, 1, 3, 32, 1225, 155106, 63602770, 85538516963, 386246934638991, 6001601072676524540, 327951891446717800997416, 64149416776011080449232990868, 45546527789182522411309599498741023, 118653450898277491435912500458608964207578 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, number of n X n rational {0,1}-matrices with no zero rows or columns and with all rows distinct, up to permutation of rows.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = Sum_{k=0..n} (-1)^k*C(n, k)*C(2^(n-k)-1, n).

a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n+1, k+1)*(2^k-1)^n.

G.f.: Sum_{n>=0} log(1+(2^n-1)*x)^n/((1+(2^n-1)*x)*n!). - Paul D. Hanna and Vladeta Jovovic, Jan 16 2008

a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jun 04 2022

MATHEMATICA

Join[{1}, Table[Sum[StirlingS1[n+1, k+1]*(2^k - 1)^n, {k, 0, n}]/n!, {n, 1, 15}]] (* Vaclav Kotesovec, Jun 04 2022 *)

CROSSREFS

Main diagonal of A055154.

Cf. A048291, A088310, A181230, A259763.

Sequence in context: A352019 A355084 A202806 * A203323 A222683 A134474

Adjacent sequences: A054777 A054778 A054779 * A054781 A054782 A054783

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, May 21 2000

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)