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A185997 Inverse of coefficient array of orthogonal polynomials P(n,x)=(x-2n+2)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1, P(1,x)=x-1.

%I A185997 #15 Apr 02 2019 05:40:42
%S A185997 1,1,1,2,3,1,5,11,7,1,16,48,44,13,1,64,244,289,129,21,1,308,1419,2045,
%T A185997 1210,306,31,1,1727,9281,15649,11447,3937,627,43,1,11008,67236,129112,
%U A185997 111890,48586,10680,1156,57,1,78244,532816,1143134,1140554,596698,168102,25293,1969,73,1,611060,4573278,10808122,12163344,7427056,2555941,497215,53954,3154,91,1
%N A185997 Inverse of coefficient array of orthogonal polynomials P(n,x)=(x-2n+2)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1, P(1,x)=x-1.
%H A185997 E. Deutsch, L. Ferrari and S. Rinaldi, <a href="https://doi.org/10.1016/j.aam.2004.05.002">Production Matrices</a>, Advances in Applied Mathematics, 34 (2005) pp. 101-122.
%e A185997 Triangle begins:
%e A185997   1,
%e A185997   1, 1,
%e A185997   2, 3, 1,
%e A185997   5, 11, 7, 1,
%e A185997   16, 48, 44, 13, 1,
%e A185997   64, 244, 289, 129, 21, 1,
%e A185997   308, 1419, 2045, 1210, 306, 31, 1,
%e A185997   1727, 9281, 15649, 11447, 3937, 627, 43, 1,
%e A185997   11008, 67236, 129112, 111890, 48586, 10680, 1156, 57, 1,
%e A185997   78244, 532816, 1143134, 1140554, 596698, 168102, 25293, 1969, 73, 1
%e A185997 Production matrix begins:
%e A185997   1, 1,
%e A185997   1, 2, 1,
%e A185997   0, 3, 4, 1,
%e A185997   0, 0, 5, 6, 1,
%e A185997   0, 0, 0, 7, 8, 1,
%e A185997   0, 0, 0, 0, 9, 10, 1,
%e A185997   0, 0, 0, 0, 0, 11, 12, 1,
%e A185997   0, 0, 0, 0, 0, 0, 13, 14, 1,
%e A185997   0, 0, 0, 0, 0, 0, 0, 15, 16, 1
%Y A185997 Cf. A178121.
%Y A185997 Inverse is A185996. First column is A185998.
%K A185997 nonn,easy,tabl
%O A185997 0,4
%A A185997 _Paul Barry_, Feb 08 2011