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A350855 a(0) = 1, a(n) = (n+1)*a(n-1) + (n-2). 0
1, 1, 3, 13, 67, 405, 2839, 22717, 204459, 2044597, 22490575, 269886909, 3508529827, 49119417589, 736791263847, 11788660221565, 200407223766619, 3607330027799157, 68539270528183999, 1370785410563679997, 28786493621837279955, 633302859680420159029, 14565965772649663657687 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ (6-2e)*(n+1)!.
E.g.f.: (exp(x)*(4*x-x^2-5)+6)/(x-1)^2. - Alois P. Heinz, Jan 19 2022
EXAMPLE
a(1) = (1+1)*a(0) + (1-2) = 2-1 = 1.
a(2) = (2+1)*a(1) + (2-2) = 3.
MATHEMATICA
Nest[Append[#1, (#2 + 1) #1[[-1]] + (#2 - 2)] & @@ {#, Length@ #} &, {1}, 20] (* Michael De Vlieger, Jan 19 2022 *)
PROG
(PARI) a(n) = if (n, (n+1)*a(n-1) + (n-2), 1); \\ Michel Marcus, Jan 19 2022
(Python)
terms = [1]
for n in range(1, 20):
terms.append((n+1)*terms[-1]+n-2)
print(terms) # Gleb Ivanov, Jan 19 2022
CROSSREFS
Cf. A020543.
Sequence in context: A107592 A215257 A367919 * A295226 A028418 A180191
KEYWORD
nonn
AUTHOR
Amrit Awasthi, Jan 19 2022
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)