A006550 n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).

0, 1, 10, 57, 234, 770, 2136, 5180, 11292, 22599, 42190, 74371, 124950, 201552, 313964, 474510, 698456, 1004445, 1414962, 1956829, 2661730, 3566766, 4715040, 6156272, 7947444, 10153475, 12847926, 16113735, 20043982, 24742684, 30325620

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 254, gives this as number of ways to color faces of a cube using at most n colors, but the formula is incorrect - see A047780.

Links

• V. Meally, Letter to N. J. A. Sloane, N.D.
• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
• Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Programs

Maple

A006550:=(-1-3*z-8*z**2-10*z**3-14*z**4+6*z**5)/(z-1)**7; # conjectured by Simon Plouffe in his 1992 dissertation

Mathematica

Table[n+8Binomial[n,2]+30Binomial[n,3]+62Binomial[n,4]+75Binomial[n,5]+ 30Binomial[n,6],{n,0,40}] (* or *) LinearRecurrence[{7,-21,35,-35, 21,-7,1}, {0,1,10,57,234,770,2136},40] (* Harvey P. Dale, Apr 24 2011 *)

Extensions

Jud McCranie found this error and gave the correct version of this sequence (A047780).