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A133710 Column l=3 of irregular triangle in A133709.

%I A133710 #15 Apr 03 2020 07:53:06
%S A133710 0,3,35,131,347,767,1511,2744,4686,7623,11919,18029,26513,38051,53459,
%T A133710 73706,99932,133467,175851,228855,294503,375095,473231,591836,734186,
%U A133710 903935,1105143,1342305,1620381,1944827
%N A133710 Column l=3 of irregular triangle in A133709.
%F A133710 Conjectures from _Colin Barker_, Apr 03 2020: (Start)
%F A133710 G.f.: x^2*(3 + 14*x - 51*x^2 + 60*x^3 - 31*x^4 + 6*x^5) / (1 - x)^7.
%F A133710 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A133710 (End)
%p A133710 A133710 := proc(m)
%p A133710         A133709(m,3) ;
%p A133710 end proc:
%p A133710 seq(A133710(m),m=1..30) ; # _R. J. Mathar_, Nov 23 2011
%t A133710 T[m_, l_] := T[m, l] = If[l == 1, 1, Sum[(-1)^i Binomial[l, i]* Binomial[2^(l - i) + m - 2, m], {i, 0, l - 1}] - Sum[StirlingS2[l, i]* T[m, i], {i, 1, l - 1}]];
%t A133710 Table[T[m, 3], {m, 1, 30}] (* _Jean-François Alcover_, Apr 03 2020 *)
%Y A133710 Cf. A133709.
%K A133710 nonn
%O A133710 1,2
%A A133710 _N. J. A. Sloane_, Dec 30 2007
%E A133710 Typo in data corrected by _Jean-François Alcover_, Apr 03 2020