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%I #21 Nov 25 2021 08:40:09
%S 1,1,3,6,21,69,342,1791,13419,111924,1306215,17423271,321771366,
%T 6890344533,203170877793,7003940931864,331467832767285,
%U 18429651200703861,1404296660000722446,126080887032762342111,15497512127400670236027,2248516102364654511363948
%N a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 1.
%H G. C. Greubel, <a href="/A135686/b135686.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = a(n-1) + A000045(n)*a(n-1), with a(1) = 1, a(2) = 1.
%p a:= proc(n) option remember; `if`(n<2, n,
%p a(n-2)*(<<0|1>, <1|1>>^n)[1, 2]+a(n-1))
%p end:
%p seq(a(n), n=1..25); # _Alois P. Heinz_, Oct 26 2016
%t RecurrenceTable[{a[1]==1,a[2]==1,a[n]==a[n-1]+Fibonacci[n+1]a[n-2]},a,{n,25}] (* _Harvey P. Dale_, Feb 07 2012 *)
%o (Sage)
%o @CachedFunction
%o def a(n): # A135686
%o if (n<3): return 1
%o else: return a(n-1) + fibonacci(n)*a(n-2)
%o [a(n) for n in (1..40)] # _G. C. Greubel_, Nov 25 2021
%Y Cf. A000045.
%K nonn,less
%O 1,3
%A _Roger L. Bagula_, Feb 18 2008
%E Corrected and edited by _Joerg Arndt_, Oct 26 2016
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