The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A332868 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A332868

Number of involutions (plus identity) in a fixed Sylow 2-subgroup of the symmetric group of degree 2n.
(history; published version)

#12 by Alois P. Heinz at Fri Apr 10 15:16:15 EDT 2020

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proposed

approved

#11 by Jean-François Alcover at Fri Apr 10 12:15:48 EDT 2020

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editing

proposed

#10 by Jean-François Alcover at Fri Apr 10 12:15:41 EDT 2020

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1, b[n - 1]^2 + 2^(2^(n - 1) - 1)];

a[n_] := Function[l, Product[If[l[[i]] == 1, b[i], 1], {i, 1, Length[l]}]][ Reverse @ IntegerDigits[n, 2]];

a /@ Range[0, 35] (* Jean-François Alcover, Apr 10 2020, after Alois P. Heinz *)

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approved

editing

#9 by Alois P. Heinz at Thu Mar 05 22:12:58 EST 2020

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editing

approved

#8 by Alois P. Heinz at Thu Mar 05 22:12:54 EST 2020

LINKS

Alois P. Heinz, <a href="/A332868/b332868.txt">Table of n, a(n) for n = 0..2412</a>

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approved

editing

#7 by Alois P. Heinz at Thu Feb 27 21:59:34 EST 2020

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editing

approved

#6 by Alois P. Heinz at Thu Feb 27 21:59:29 EST 2020

MAPLE

b:= proc(n) b(n):=`if`(n=0, 1, b(n-1)^2+2^(2^(n-1)-1)) end:

a:= n-> (l-> mul(`if`(l[i]=1, b(i), 1), i=1..nops(l)))(Bits[Split](n)):

seq(a(n), n=0..35); # Alois P. Heinz, Feb 27 2020

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editing

#5 by Andrew Howroyd at Thu Feb 27 21:44:26 EST 2020

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proposed

#4 by Andrew Howroyd at Thu Feb 27 21:28:03 EST 2020

DATA

1, 2, 6, 12, 44, 88, 264, 528, 2064, 4128, 12384, 24768, 90816, 181632, 544896, 1089792, 4292864, 8585728, 25757184, 51514368, 188886016, 377772032, 1133316096, 2266632192, 8860471296, 17720942592, 53162827776, 106325655552, 389860737024, 779721474048, 2339164422144

PROG

(PARI) a(n)={my(v=vector(logint(max(1, n), 2)+1)); v[1]=2; for(n=2, #v, v[n]=v[n-1]^2 + 2^(2^(n-1)-1)); prod(k=1, #v, if(bittest(n, k-1), v[k], 1))} \\ Andrew Howroyd, Feb 27 2020

CROSSREFS

Cf. A332757, A332759.

EXTENSIONS

Terms a(17) and beyond from Andrew Howroyd, Feb 27 2020

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proposed

editing

#3 by Nick Krempel at Thu Feb 27 19:23:14 EST 2020

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editing

proposed