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A048631 Xfactorials - like factorials but use carryless GF(2)[ X ] polynomial multiplication. 7
1, 1, 2, 6, 24, 120, 272, 1904, 15232, 124800, 848640, 7507200, 39738368, 433441792, 2589116416, 30419859456, 486717751296, 8128101580800, 132557598294016, 1971862458400768, 30421253686034432, 512675443057623040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In formula X stands for the multiplication in a ring of GF(2)[ X ] polynomials.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..475

Vaclav Kotesovec, Graph a(n+1)/a(n)

FORMULA

a(0) = 1, a(n) = n X a(n-1) (see the Maple function Xfactorial given below).

MAPLE

Xfactorial := proc(n); if(0 = n) then RETURN(1); else RETURN(Xmult(n, Xfactorial(n-1))); fi; end;

Xmult := proc(n, m) option remember; if(0 = n) then RETURN(0); else RETURN(XORnos(((n mod 2)*m), Xmult(floor(n/2), m*2))); fi; end;

MATHEMATICA

Xmult[nn_, mm_] := Module[{n = nn, m = mm, s = 0}, While[n > 0, If[1 == Mod[n, 2], s = BitXor[s, m]]; n = Floor[n/2]; m = m*2]; s];

Xfactorial[n_] := Xfactorial[n] = If[0 == n, 1, Xmult[n, Xfactorial[n - 1]] ];

Table[Xfactorial[n], {n, 0, 21}] (* Jean-Fran├žois Alcover, Mar 04 2016, updated Mar 06 2016 after Maple *)

PROG

(PARI) a(n)=my(s=Mod(1, 2)); for(k=1, n, s*=Pol(binary(k))); fromdigits(Vec(lift(s)), 2) \\ Charles R Greathouse IV, Oct 03 2016

CROSSREFS

Cf. A000142, A048720, A048632, A061922.

Sequence in context: A083267 A130480 A000804 * A263700 A263701 A263702

Adjacent sequences:  A048628 A048629 A048630 * A048632 A048633 A048634

KEYWORD

easy,nonn

AUTHOR

Antti Karttunen, Jul 14 1999

STATUS

approved

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Last modified December 14 01:27 EST 2019. Contains 329978 sequences. (Running on oeis4.)