A003874 - OEIS

%I #24 Sep 23 2024 10:13:42

%S 1,1,9,9,35,35,36,36,42,42,75,75,84,84,90,90,126,126,160,160,210,210,

%T 225,225,252,252,288,288,300,300,315,315,350,350,448,450,450,525,525,

%U 567,567,768

%N Degrees of irreducible representations of symmetric group S_10.

%C All 42 terms of this finite sequence are shown.

%D 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].

%t 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}]];

%t 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 T[n_] := g[n, n, {}];

%t Sort[T[10]] (* _Jean-François Alcover_, Sep 23 2024, after _Alois P. Heinz_ in A060240 *)

%o (Magma) // See A003875 for Magma code.

%o (GAP) A003874 := List(Irr(CharacterTable("S10")), chi->chi[1]);; Sort(A003874); # _Eric M. Schmidt_, Jul 18 2012

%Y Row n=10 of A060240.

%K nonn,fini,full

%O 1,3

%A _N. J. A. Sloane_