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 A305737 Number of subsets S of vectors in GF(2)^n such that span(S) = GF(2)^n. 1
 1, 2, 8, 184, 62464, 4293001088, 18446743803209556992, 340282366920938461120638132973980614656, 115792089237316195423570985008687907766497981100801256254562260326801824546816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Asymptotic to A001146(n) = 2^(2^n). REFERENCES R. P. Stanley, Enumerative Combinatorics Vol 1, Cambridge, 1997, page 127. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..10 FORMULA a(n) = Sum_{k=0..n} A022166(n,k)*(-1)^(n-k)*2^binomial(n-k,2)*(2^(2^k)-1). MATHEMATICA Table[Sum[QBinomial[n, k, q] (-1)^(n - k) q^Binomial[n - k, 2] (2^(q^k) - 1) /. q -> 2, {k, 0, n}], {n, 0, 8}] PROG (PARI) \\ here U(n, k) is A022166(n, k). U(n, k)={polcoeff(x^k/prod(j=0, k, 1-2^j*x+x*O(x^n)), n)} a(n)={sum(k=0, n, U(n, k)*(-1)^(n-k)*2^binomial(n-k, 2)*(2^(2^k)-1))} \\ Andrew Howroyd, Mar 01 2020 CROSSREFS Cf. A001146, A022166. Sequence in context: A181234 A156526 A009505 * A028368 A056990 A234637 Adjacent sequences:  A305734 A305735 A305736 * A305738 A305739 A305740 KEYWORD nonn AUTHOR Geoffrey Critzer, Jun 22 2018 EXTENSIONS a(8) corrected by Andrew Howroyd, Mar 01 2020 STATUS approved

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Last modified January 21 16:02 EST 2021. Contains 340352 sequences. (Running on oeis4.)