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,...

1, 2, 3, 5, 20, 19, 12, 90, 214, 160, 29, 348, 1497, 2718, 1744, 70, 1225, 8236, 26453, 40336, 23184, 169, 4056, 39114, 193184, 512813, 689512, 364176, 408, 12852, 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

Offset

1,2

Links

Table of n, a(n) for n=1..55.

K. S. Brown, Integer Sequences Related To Pi

Example

For j=1,2,3 the polynomials P(k) are 1, 3 + 2 k, 19 + 20 k + 5 k^2.
1;
2,3,
5,20,19,
12,90,214,160,
29,348,1497,2718,1744,
70,1225,8236,26453,40336,23184,
169,4056,39114,193184,512813,689512,364176,
408,12852,167884,1174860,4737628,10955304,13372072,6598656,
985,39400,669078,6282340,35554929,123708580,257200712,290478120,135484416,
2378,117711,2519024,30514946,229958030,1114357079,3459179856,6602445344,6991966752,3108695040,

Crossrefs

Sequence in context: A106047 A048826 A321084 * A127078 A184252 A228833

Adjacent sequences: A054795 A054796 A054797 * A054799 A054800 A054801

Keyword

nonn,easy,tabl

Author

N. J. A. Sloane, May 26 2000

Extensions

Sign corrected by R. J. Mathar, Jul 13 2013

Status

approved