A392898 - OEIS

%I #71 Jul 05 2026 15:54:45

%S 0,1,3,10,37,167,924,6131,47375,416386,4092561,44425747,527519908,

%T 6798966455,94504777563,1408978112018,22426272777581,379522678985599,

%U 6804322657491180,128828945745308779,2568535276579439959,53788306394034188738,1180357569448221308697

%N a(n) = a(n-1) + a(n-2) + n! with a(0)=0, a(1)=1.

%H Harvey P. Dale, <a href="/A392898/b392898.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = Sum_{i=1..n} Fibonacci(n-i+1)*i!.

%F a(n) = A192744(n) + A192745(n) - Fibonacci(n+1).

%F a(n) = (n+1)*a(n-1) - (n-1)*a(n-2) - n*a(n-3) for n>=3. - _Alois P. Heinz_, Jan 27 2026

%p a := proc(n) option remember; if n<2 then n else a(n-1)+a(n-2)+n! fi end:

%p seq(a(n), n=0..22);

%t a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + n!; Array[a,30,0]

%t nxt[{n_,a_,b_}]:={n+1,b,b+a+(n+1)!}; NestList[nxt,{1,0,1},30][[;;,2]] (* _Harvey P. Dale_, Jul 05 2026 *)

%o (Python)

%o def generate_seq(n_terms):

%o     import math

%o     a = [0, 1]

%o     for n in range(2, n_terms):

%o         a.append(a[n-1] + a[n-2] + math.factorial(n))

%o     return a

%Y Cf. A000045, A000142, A001924, A192963, A192744, A192745.

%K nonn,easy,changed

%O 0,3

%A _Yağızhan Metin_, Jan 26 2026

%E First Mathematica program corrected by _Harvey P. Dale_, Jul 05 2026