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A054798 Let N(k) and D(k) be the sequences defined in A054765 and A012244; write N(k)* D(k+j ) - N(k+j)*D(k) = (-1)^(k+1)*(k!)^2*P(k) where P(k) is a polynomial in k of degree j-1; sequence gives coefficients of expansion of P(k) in powers of k for j=1,2,3,...

%I A054798 #14 Aug 15 2020 16:02:42
%S A054798 1,2,3,5,20,19,12,90,214,160,29,348,1497,2718,1744,70,1225,8236,26453,
%T A054798 40336,23184,169,4056,39114,193184,512813,689512,364176,408,12852,
%U A054798 167884,1174860,4737628,10955304,13372072,6598656,985,39400,669078,6282340,35554929,123708580,257200712,290478120,135484416,2378,117711,2519024,30514946,229958030,1114357079,3459179856,6602445344,6991966752,3108695040
%N A054798 Let N(k) and D(k) be the sequences defined in A054765 and A012244; write N(k)* D(k+j ) - N(k+j)*D(k) = (-1)^(k+1)*(k!)^2*P(k) where P(k) is a polynomial in k of degree j-1; sequence gives coefficients of expansion of P(k) in powers of k for j=1,2,3,...
%H A054798 K. S. Brown, <a href="https://www.mathpages.com/home/kmath381/kmath381.htm">Integer Sequences Related To Pi</a>
%e A054798 For j=1,2,3 the polynomials P(k) are 1, 3 + 2 k, 19 + 20 k + 5 k^2.
%e A054798 1;
%e A054798 2,3,
%e A054798 5,20,19,
%e A054798 12,90,214,160,
%e A054798 29,348,1497,2718,1744,
%e A054798 70,1225,8236,26453,40336,23184,
%e A054798 169,4056,39114,193184,512813,689512,364176,
%e A054798 408,12852,167884,1174860,4737628,10955304,13372072,6598656,
%e A054798 985,39400,669078,6282340,35554929,123708580,257200712,290478120,135484416,
%e A054798 2378,117711,2519024,30514946,229958030,1114357079,3459179856,6602445344,6991966752,3108695040,
%K A054798 nonn,easy,tabl
%O A054798 1,2
%A A054798 _N. J. A. Sloane_, May 26 2000
%E A054798 Sign corrected by _R. J. Mathar_, Jul 13 2013