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A115376 where h[d+1,d-1] is a homogeneous symmetric function, s[d,d] is a Schur function indexed by two parts, * represents the Kronecker product and <, > is the standard scalar product on symmetric functions.

%I A115376 #12 May 10 2019 08:36:02
%S A115376 1,1,5,6,16,20,41,51,90,111,177,216,321,387,546,651,882,1041,1366,
%T A115376 1597,2042,2367,2962,3407,4187,4782,5787,6567,7842,8847,10443,11718,
%U A115376 13692,15288,17703,19677,22603,25018,28532,31458,35644,39158,44108,48294
%N A115376 <h[d+1,d-1],s[d,d]*s[d,d]*s[d,d]> where h[d+1,d-1] is a homogeneous symmetric function, s[d,d] is a Schur function indexed by two parts, * represents the Kronecker product and <, > is the standard scalar product on symmetric functions.
%H A115376 Colin Barker, <a href="/A115376/b115376.txt">Table of n, a(n) for n = 2..1000</a>
%H A115376 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-7,2,8,2,-7,-3,4,1,-1).
%F A115376 G.f.: x^2 / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)).
%F A115376 a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 7*a(n-4) + 2*a(n-5) + 8*a(n-6) + 2*a(n-7) - 7*a(n-8) - 3*a(n-9) + 4*a(n-10) + a(n-11) - a(n-12) for n>11. - _Colin Barker_, May 10 2019
%t A115376 Drop[CoefficientList[Series[x^2/((1-x)(1-x^2)^4(1-x^3)),{x,0,50}],x],2]  (* _Harvey P. Dale_, Aug 24 2011 *)
%o A115376 (PARI) Vec(x^2 / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)) + O(x^50)) \\ _Colin Barker_, May 10 2019
%Y A115376 Cf. A115375, A082424, A008763, A082437.
%K A115376 nonn,easy
%O A115376 2,3
%A A115376 _Mike Zabrocki_, Jan 21 2006