A054798 - OEIS

%I #14 Aug 15 2020 16:02:42

%S 1,2,3,5,20,19,12,90,214,160,29,348,1497,2718,1744,70,1225,8236,26453,

%T 40336,23184,169,4056,39114,193184,512813,689512,364176,408,12852,

%U 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 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 K. S. Brown, <a href="https://www.mathpages.com/home/kmath381/kmath381.htm">Integer Sequences Related To Pi</a>

%e For j=1,2,3 the polynomials P(k) are 1, 3 + 2 k, 19 + 20 k + 5 k^2.

%e 1;

%e 2,3,

%e 5,20,19,

%e 12,90,214,160,

%e 29,348,1497,2718,1744,

%e 70,1225,8236,26453,40336,23184,

%e 169,4056,39114,193184,512813,689512,364176,

%e 408,12852,167884,1174860,4737628,10955304,13372072,6598656,

%e 985,39400,669078,6282340,35554929,123708580,257200712,290478120,135484416,

%e 2378,117711,2519024,30514946,229958030,1114357079,3459179856,6602445344,6991966752,3108695040,

%K nonn,easy,tabl

%O 1,2

%A _N. J. A. Sloane_, May 26 2000

%E Sign corrected by _R. J. Mathar_, Jul 13 2013