A003872 Degrees of irreducible representations of symmetric group S_8.

1, 1, 7, 7, 14, 14, 20, 20, 21, 21, 28, 28, 35, 35, 42, 56, 56, 64, 64, 70, 70, 90

Offset

1,3

Comments

All 22 terms of this finite sequence are shown.

References

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].

Links

Table of n, a(n) for n=1..22.

Mathematica

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]], If[i < 1, 0, Flatten@ Table[g[n - i*j, i - 1, Join[l, Array[i &, j]]], {j, 0, n/i}]]];
T[n_] := g[n, n, {}];
Sort[T[8]] (* Jean-François Alcover, Sep 22 2024, after Alois P. Heinz in A060240 *)

Prog

(GAP) A003872 := List(Irr(CharacterTable("S8")), chi->chi[1]);; Sort(A003872); # Eric M. Schmidt, Jul 18 2012

Crossrefs

Row n=8 of A060240.

Sequence in context: A040043 A339706 A355897 * A168374 A112438 A309459

Adjacent sequences: A003869 A003870 A003871 * A003873 A003874 A003875

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved