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A046682
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Number of cycle types of even permutations; also number of conjugacy classes of partitions of n.
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18
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1, 1, 1, 2, 3, 4, 6, 8, 12, 16, 22, 29, 40, 52, 69, 90, 118, 151, 195, 248, 317, 400, 505, 632, 793, 985, 1224, 1512, 1867, 2291, 2811, 3431, 4186, 5084, 6168, 7456, 9005, 10836, 13026, 15613, 18692, 22316, 26613, 31659, 37619, 44601, 52815, 62416, 73680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also number of partitions of n with even number of even parts. There is no restriction on the odd parts.
a(n) = u(n) + v(n), n>=2, of the Osima reference, p. 383.
Also number of partitions of n with largest part congruent to n modulo 2: a(2*n)=A027187(2*n), a(2*n-1)=A027193(2*n-1); a(n)=A000041(n)-A000701(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 22 2006
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REFERENCES
| M. Osima, On the irreducible representations of the symmetric group, Canad. J. Math., 4 (1952), 381-384.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
| G.f.: (Sum (-q^2)^(n^2), n =0 .. inf )/(product_{m=1..inf} (1-q^m)); or (product_{m=1..inf} (1-q^m)^(-1) + product_{m=1.. inf} (1+q^(2*m-1)) )/2. - Mamuka Jibladze (jib(AT)rmi.acnet.ge), Sep 07 2003
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MATHEMATICA
| max = 48; f[q_] := Sum[(-q^2)^n^2, {n, 0, max}]/Product[1-q^n, {n, 1, max}]; CoefficientList[ Series[f[q], {q, 0, max}], q] (* From Jean-François Alcover, Oct 18 2011, after g.f. *)
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PROG
| (PARI) list(lim)=my(q='q); Vec(sum(n=0, sqrt(lim), (-q^2)^(n^2))/prod(n=1, lim, 1-q^n)+O(q^(lim\1+1))) \\ Charles R Greathouse IV, Oct 18 2011
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CROSSREFS
| a(n)=(A000041(n)+A000700(n))/2. Cf. A000701, A006950, A015128.
For the number of conjugacy classes of the alternating group A_n, n>=2, see A000702.
Cf. A118301.
Sequence in context: A018718 A036451 A180652 * A005987 A125895 A064428
Adjacent sequences: A046679 A046680 A046681 * A046683 A046684 A046685
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KEYWORD
| nonn,nice
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs)
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