A003871 - OEIS

A003871

Degrees of irreducible representations of symmetric group S_7.

1, 1, 6, 6, 14, 14, 14, 14, 15, 15, 20, 21, 21, 35, 35

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OFFSET

1,3

COMMENTS

All 15 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..15.

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[7]] (* Jean-François Alcover, Sep 22 2024, after Alois P. Heinz in A060240 *)

PROG

(GAP) A003871 := List(Irr(CharacterTable("S7")), chi->chi[1]);; Sort(A003871); # Eric M. Schmidt, Jul 18 2012

CROSSREFS

Row n=7 of A060240.

Sequence in context: A214828 A229828 A141378 * A220698 A315802 A315803

Adjacent sequences: A003868 A003869 A003870 * A003872 A003873 A003874

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane

STATUS

approved