A392898 a(n) = a(n-1) + a(n-2) + n! with a(0)=0, a(1)=1.

0, 1, 3, 10, 37, 167, 924, 6131, 47375, 416386, 4092561, 44425747, 527519908, 6798966455, 94504777563, 1408978112018, 22426272777581, 379522678985599, 6804322657491180, 128828945745308779, 2568535276579439959, 53788306394034188738, 1180357569448221308697

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..449

Formula

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

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

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

Maple

a := proc(n) option remember; if n<2 then n else a(n-1)+a(n-2)+n! fi end:
seq(a(n), n=0..22);

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + n!; Array[a, 30, 0]
nxt[{n_, a_, b_}]:={n+1, b, b+a+(n+1)!}; NestList[nxt, {1, 0, 1}, 30][[;; , 2]] (* Harvey P. Dale, Jul 05 2026 *)

Prog

(Python)
def generate_seq(n_terms):
    import math
    a = [0, 1]
    for n in range(2, n_terms):
        a.append(a[n-1] + a[n-2] + math.factorial(n))
    return a

Crossrefs

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

Sequence in context: A363294 A289990 A370369 * A123636 A375655 A371901

Adjacent sequences: A392895 A392896 A392897 * A392899 A392900 A392901

Keyword

nonn,easy,changed

Author

Yağızhan Metin, Jan 26 2026

Extensions

First Mathematica program corrected by Harvey P. Dale, Jul 05 2026

Status

approved