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A056162
a(n) = Sum_{k=0..n} (k!)^(n-k).
1
1, 2, 3, 5, 13, 71, 931, 30275, 2591059, 614059331, 423463272451, 907403624202755, 6082394749206781699, 140440480114401911810051, 10845109029138237198786147331, 3088811811740393517911301490890755, 3220352134317904958924570965080200574979
OFFSET
0,2
LINKS
FORMULA
G.f.: Sum_{k>=0} x^k/(1 - k!*x). - Ilya Gutkovskiy, Oct 09 2018
log(a(n)) ~ log(n) * ((2*n+1)*log(n) - 2*n) * ((2*n*log(2*n-1) + 2*n*log(log(n)) - (2*n+1) * log(2*log(n)-1) - 2*n*(1+log(2))) / (4*(2*log(n)-1)^2)). - Vaclav Kotesovec, Oct 10 2018
EXAMPLE
a(5) = (0!)^5 + (1!)^4 + (2!)^3 + (3!)^2 + (4!)^1 + (5!)^0 = 1 + 1 + 8 + 36 + 24 + 1 = 71.
MAPLE
a:=n->add(factorial(k)^(n-k), k=0..n): seq(a(n), n=0..16); # Muniru A Asiru, Oct 09 2018
MATHEMATICA
Table[Sum[(k!)^(n-k), {k, 0, n}], {n, 0, 16}] (* Vaclav Kotesovec, Oct 09 2018 *)
PROG
(GAP) List([0..16], n->Sum([0..n], k->Factorial(k)^(n-k))); # Muniru A Asiru, Oct 09 2018
(Magma) [&+[Factorial(k)^(n-k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Oct 10 2018
(PARI) a(n) = sum(k=0, n, k!^(n-k)); \\ Michel Marcus, Oct 10 2018
CROSSREFS
Sequence in context: A042695 A288943 A074394 * A265785 A326372 A001685
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Jul 31 2000
EXTENSIONS
a(15)-a(16) from Ilya Gutkovskiy, Oct 09 2018
STATUS
approved