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%I #15 Mar 28 2024 11:46:09
%S 1,6,25,132,824,5932,48444,442916,4484524,49828044,602919332,
%T 7892762164,111156400476,1675896499484,26934050884564,459674468429892,
%U 8302870086014924,158242935756990316,3173649989348528004
%N a(1)=1; for n > 1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + 4.
%C More generally, if m is an integer and a(1)=1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + m then a(n) has a closed form formula as a(n) = floor/ceiling(n*r(m)*n!) where r(m) = frac(e*m) + 0 or + 1/2 or -1/2 + integer. (See Example section.)
%H Harvey P. Dale, <a href="/A082430/b082430.txt">Table of n, a(n) for n = 1..448</a>
%F For n >= 2, a(n) = ceiling(n*(19/2 - 4*e)*n!).
%e r(10) = frac(10*e) + 1/2 + 2;
%e r(12) = frac(12*e) - 1/2 + 3;
%e r(15) = frac(15*e) + 3;
%e r(18) = frac(18*e) - 1/2 + 4.
%t nxt[{n_,t_,a_}]:=Module[{c=t(n+1)+4},{n+1,t+c,c}]; NestList[nxt,{1,1,1},20][[;;,3]] (* _Harvey P. Dale_, Mar 28 2024 *)
%Y Cf. A007808, A074143.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Apr 24 2003
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