A007566 a(n+1) = (2n+3)*a(n) - 2n*a(n-1) + 8n, a(0) = 1, a(1) = 3.

1, 3, 21, 151, 1257, 12651, 151933, 2127231, 34035921, 612646867, 12252937701, 269564629863, 6469551117241, 168208329048891, 4709833213369677, 141294996401091151, 4521439884834917793, 153728956084387206051, 5534242419037939419061, 210301211923441697925687

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			1 + 3*x + 21*x^2 + 151*x^3 + 1257*x^4 + 12651*x^5 + 151933*x^6 + 2127231*x^7 + ...
		

References

• M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 36. [From N. J. A. Sloane, Jan 29 2009]
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. Doster, Problem 10403, Amer. Math. Monthly, Vol. 101 (1994), p. 792; Solution, Vol. 104 (1997), p. 368.

Crossrefs

Cf. A010844.

Programs

Maple

a:=proc(n) option remember; if n = 0 then RETURN(1); fi; if n = 1 then RETURN(3); fi; (2*n+1)*a(n-1)-(2*n-2)*a(n-2) + 8*(n-1); end;

Formula

a(n) = 2*n*a(n-1) + (2*n-1)^2 = 2 * floor(e^(1/2) * n! * 2^n) - (2*n+1) = 2*A010844(n) - (2n+1). - Michael Somos, Mar 26 1999