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A123235 Triangle of coefficients p(k, x), where p(k, x) = 2*(k-1)*p(k-1, x) -x*p(k-2, x), read by rows.

%I A123235 #15 Nov 23 2019 21:09:29
%S A123235 1,1,1,2,1,8,3,-1,48,16,-7,384,120,-59,1,3840,1152,-606,17,46080,
%T A123235 13440,-7392,263,-1,645120,184320,-104640,4288,-31,10321920,2903040,
%U A123235 -1687680,76000,-759,1,185794560,51609600,-30562560,1472640,-17950,49
%N A123235 Triangle of coefficients p(k, x), where p(k, x) = 2*(k-1)*p(k-1, x) -x*p(k-2, x), read by rows.
%C A123235 Row sums give A093856.
%D A123235 Eugene Jahnke and Fritz Emde, Table of Functions with Formulae and Curves, Dover Book, New York, 1945, page 144.
%H A123235 G. C. Greubel, <a href="/A123235/b123235.txt">Rows n = 0..30 of triangle, flattened</a>
%F A123235 Coefficient list of the polynomials p(k, x) = 2*(k-1)*p(k-1, x) - x*p(k - 2, x), with p(0, x) = 1 and p(1, x) = 1 + x.
%e A123235 Triangle begins as:
%e A123235       1;
%e A123235       1,     1;
%e A123235       2,     1;
%e A123235       8,     3,    -1;
%e A123235      48,    16,    -7;
%e A123235     384,   120,   -59,   1;
%e A123235    3840,  1152,  -606,  17;
%e A123235   46080, 13440, -7392, 263, -1;
%t A123235 p[n_, x_]:= p[n, x]= If[n==0, 1, If[n==1, x+1, 2*(n-1)*p[n-1, x] -x*p[n-2, x]]]; Table[CoefficientList[p[n, x], x], {n, 0, 10}]//Flatten
%Y A123235 Cf. A093856.
%K A123235 tabf,sign
%O A123235 0,4
%A A123235 _Roger L. Bagula_, Oct 06 2006
%E A123235 Edited by _G. C. Greubel_, Nov 22 2019