A090809 Coefficient of the irreducible character of S_m indexed by (m-2n+2,2n-2) in the n-th Kronecker power of the representation indexed by (m-2,2).

0, 0, 2, 10, 31, 75, 155, 287, 490, 786, 1200, 1760, 2497, 3445, 4641, 6125, 7940, 10132, 12750, 15846, 19475, 23695, 28567, 34155, 40526, 47750, 55900, 65052, 75285, 86681, 99325, 113305, 128712, 145640, 164186, 184450, 206535, 230547

Offset: 0

Author

Alain Goupil, Feb 10 2004

Keywords

• nonn
• easy

Comments

For n > 0, the terms of this sequence are related to A000124 by a(n) = Sum_{i=0..n-1} i*A000124(i). - Bruno Berselli, Dec 20 2013

References

• A. Goupil, Combinatorics of the Kronecker products of irreducible representations of Sn, in preparation.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000124, A049020.

Programs

Maple

f := proc(k) 2*binomial(k,2)+4*binomial(k,3)+3*binomial(k,4); end;
seq (f(n), n=0..50);

Mathematica

f[n_] := 2Binomial[n, 2] + 4Binomial[n, 3] + 3Binomial[n, 4]; Table[ f[n], {n, 0, 40}] (* Robert G. Wilson v, Feb 13 2004 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 2, 10, 31}, 38] (* Jean-François Alcover, Sep 25 2017 *)

Formula

a(n) = 2*binomial(n, 2) + 4*binomial(n, 3) + 3*binomial(n, 4) = (n-1)*n*(3*n^2 + n + 10)/24.

a(n) = A049020(n, n-2), for n >= 2. - Philippe Deléham, Mar 06 2004

G.f.: x^2*(2 + x^2) / (1-x)^5. - Colin Barker, Nov 21 2012

Extensions

More terms from Robert G. Wilson v, Feb 13 2004