A007566 a(n+1) = (2n+3)*a(n) - 2n*a(n-1) + 8n, a(0) = 1, a(1) = 3. (Formerly M3081)

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

Offset

0,2

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

Table of n, a(n) for n=0..19.

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

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

Example

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

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;

Crossrefs

Cf. A010844.

Sequence in context: A037768 A037656 A074577 * A183412 A155627 A163472

Adjacent sequences: A007563 A007564 A007565 * A007567 A007568 A007569

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved