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A006277
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a(n) = (a(n-1) + 1)*a(n-2).
(Formerly M0888)
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7
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1, 1, 2, 3, 8, 27, 224, 6075, 1361024, 8268226875, 11253255215681024, 93044467205527772332546875, 1047053135870867396062743192203958743681024, 97422501162981936223682742789520433197690551802305989766350860546875
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 6.7.
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.10 Quadratic recurrence constants, pp. 445-446.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MAPLE
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A006277 := proc(n) options remember; if n <= 1 then RETURN(1) else A006277(n-2)*(A006277(n-1)+1); fi; end;
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MATHEMATICA
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RecurrenceTable[{a[n]==a[n-2]*(1+a[n-1]), a[0]==1, a[1]==1}, a, {n, 0, 15}] (* Vaclav Kotesovec, Jan 19 2015 *)
nxt[{a_, b_}]:={b, a(b+1)}; NestList[nxt, {1, 1}, 15][[All, 1]] (* Harvey P. Dale, Jun 20 2021 *)
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PROG
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(Haskell)
a006277_list = 1 : scanl ((*) . (+ 1)) 2 a006277_list -- Jack Willis, Dec 22 2013
(Maxima) a(n) := if (n = 0 or n = 1) then 1 else a(n-2)*(a(n-1)+1) $
(Magma) [n le 2 select 1 else (Self(n-1) + 1)*Self(n-2): n in [1..15]]; // Vincenzo Librandi, May 23 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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