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A171509 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126931.

%I A171509 #14 Oct 12 2024 01:40:32
%S A171509 1,3,1,10,6,1,33,29,9,1,110,126,57,12,1,366,518,306,94,15,1,1220,2052,
%T A171509 1494,600,140,18,1,4065,7925,6849,3389,1035,195,21,1,13550,30030,
%U A171509 30025,17628,6635,1638,259,24,1
%N A171509 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126931.
%C A171509 Equal to A053121*B^3, B = A007318.
%F A171509 Sum_{k=0..n} T(n,k)*x^k = A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -4, -3, -2, -1, 0 respectively.
%F A171509 T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + Sum_{i>=0} T(n-1,k+1+i)*(-3)^i. - _Philippe Deléham_, Feb 23 2012
%e A171509 Triangle begins:
%e A171509   1 ;
%e A171509   3,1 ;
%e A171509   10,6,1 ;
%e A171509   33,29,9,1 ;
%e A171509   110,126,57,12,1 ; ...
%Y A171509 Cf. A053121, A054336, A096164, A171505.
%K A171509 nonn,tabl
%O A171509 0,2
%A A171509 _Philippe Deléham_, Dec 10 2009