|
%I #31 Jan 25 2020 00:43:10
%S 0,0,2,10,31,75,155,287,490,786,1200,1760,2497,3445,4641,6125,7940,
%T 10132,12750,15846,19475,23695,28567,34155,40526,47750,55900,65052,
%U 75285,86681,99325,113305,128712,145640,164186,184450,206535,230547
%N 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).
%C 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
%D A. Goupil, Combinatorics of the Kronecker products of irreducible representations of Sn, in preparation.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 2*binomial(n, 2) + 4*binomial(n, 3) + 3*binomial(n, 4) = (n-1)*n*(3*n^2 + n + 10)/24.
%F a(n) = A049020(n, n-2), for n >= 2. - _Philippe Deléham_, Mar 06 2004
%F G.f.: x^2*(2 + x^2) / (1-x)^5. - _Colin Barker_, Nov 21 2012
%p f := proc(k) 2*binomial(k,2)+4*binomial(k,3)+3*binomial(k,4); end;
%p seq (f(n), n=0..50);
%t f[n_] := 2Binomial[n, 2] + 4Binomial[n, 3] + 3Binomial[n, 4]; Table[ f[n], {n, 0, 40}] (* _Robert G. Wilson v_, Feb 13 2004 *)
%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 2, 10, 31}, 38] (* _Jean-François Alcover_, Sep 25 2017 *)
%Y Cf. A000124, A049020.
%K nonn,easy
%O 0,3
%A _Alain Goupil_, Feb 10 2004
%E More terms from _Robert G. Wilson v_, Feb 13 2004
|
