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 A176408 a(n) = (n+1)*(a(n-1) +a(n-2)) n>1, a(0)=1,a(1)=0 6

%I #10 Nov 25 2017 09:29:04

%S 1,0,3,12,75,522,4179,37608,376083,4136910,49642923,645357996,

%T 9035011947,135525179202,2168402867235,36862848742992,663531277373859,

%U 12607094270103318

%N a(n) = (n+1)*(a(n-1) +a(n-2)) n>1, a(0)=1,a(1)=0

%C a(n) is one of two "basis" sequences for sequences of the form s(0)=a,s(1)=b,s(n)=(n+1)(s(n-1)+s(n-2)), n>1, the other being A006347.

%C s(n) = a*a(n) + b* A006347(n+1).

%C s(n) = 1/2*(b-2*a)(n+2)! +(3*a-b)*floor(((n+2)!+1)/e).

%H Indranil Ghosh, <a href="/A176408/b176408.txt">Table of n, a(n) for n = 0..447</a>

%H Michael Wallner, <a href="https://arxiv.org/abs/1706.07163">A bijection of plane increasing trees with relaxed binary trees of right height at most one</a>, arXiv:1706.07163 [math.CO], 2017, Table 2 on p. 13.

%F a(n) = 3*floor(((n+2)!+1)/e) - (n+2)!.

%F a(n) = 3* A000166(n+1) - (n+2)!, where A000166 are the subfactorial numbers.

%e a(2)= 3*9-24=3, a(3)= 3*44-120=12, a(4)= 3*265-720=75, ...

%p seq(3*floor(((n+2)!+1)/E) - (n+2)!,n=1..20);

%Y Cf. A000166, A006347.

%K nonn

%O 0,3

%A _Gary Detlefs_, Apr 16 2010

%E Data section corrected by _Indranil Ghosh_, Feb 15 2017

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)