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A007566
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a(n+1) = (2n+3)*a(n) - 2n*a(n-1) + 8n, a(0) = 1, a(1) = 3.
(Formerly M3081)
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3
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1, 3, 21, 151, 1257, 12651, 151933, 2127231, 34035921, 612646867, 12252937701, 269564629863, 6469551117241, 168208329048891, 4709833213369677, 141294996401091151, 4521439884834917793, 153728956084387206051, 5534242419037939419061, 210301211923441697925687
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. Doster, Problem 10403, Amer. Math. Monthly, Vol. 101 (1994), p. 792; Solution, Vol. 104 (1997), p. 368.
M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 36. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n) = 2n*a(n-1) + (2n-1)^2; a(n) = 2[e^(1/2)n!2^n] - (2n+1).
a(n) = 2*A010844(n) - (2n+1).
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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;
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CROSSREFS
| Sequence in context: A037768 A037656 A074577 * A183412 A155627 A163472
Adjacent sequences: A007563 A007564 A007565 * A007567 A007568 A007569
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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