A089248 a(n) is the sum of the odd degrees of the irreducible representations of the symmetric group S_n.

1, 2, 2, 8, 12, 40, 144, 128, 644, 3504, 7000, 48224, 130992, 861792, 3257600, 32768, 425988, 5833312, 27621672, 415526656, 1987852432, 17674429440, 157807273408, 265515959680, 2848581615344, 30980959604096, 114059874705248, 1365388896050048, 6215927122198944

Offset

1,2

Comments

a(n) is divisible by 4 for n >= 4. - Eric M. Schmidt, Apr 28 2013

References

John McKay, Irreducible representations of odd degree, Journal of Algebra 20, 1972 pages 416-418.

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..200

Eric M. Schmidt, Sage code to compute this sequence

Formula

a(2^n) = 2^(2^n - 1). - Eric M. Schmidt, Apr 28 2013

Prog

(Sage)
# Simple but inefficient; see links for faster code
def A089248(n) :
    res = 0
    for P in Partitions(n) :
        deg = P.dimension()
        if is_odd(deg) : res += deg
    return res
# Eric M. Schmidt, Apr 28 2013

Crossrefs

Cf. A000085, A059867.

Sequence in context: A014236 A087955 A026537 * A006663 A094941 A002785

Adjacent sequences: A089245 A089246 A089247 * A089249 A089250 A089251

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Dec 11 2003

Extensions

More terms from Eric M. Schmidt, Apr 28 2013

Status

approved