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A320962
a(n) = (-1)^(n-1)*(n-1)!*Sum_{i=0..n} Stirling2(n, i) if n > 0 and 0 otherwise.
7
0, 1, -2, 10, -90, 1248, -24360, 631440, -20865600, 852647040, -42085008000, 2462394816000, -168193308729600, 13241729554099200, -1188734048799897600, 120563962753538304000, -13704613258628388096000, 1733764260005567741952000, -242606144946628642443264000
OFFSET
0,3
COMMENTS
Also the exponential limit as defined in A320956 of log(x + 1).
EXAMPLE
Illustration of the convergence in the sense of A320956:
[0] 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
[1] 0, 1, -1, 2, -6, 24, -120, 720, -5040, ... A133942
[2] 0, 1, -2, 8, -48, 384, -3840, 46080, -645120, ... A000165
[3] 0, 1, -2, 10, -84, 984, -14640, 262800, -5513760, ... A321398
[4] 0, 1, -2, 10, -90, 1224, -22440, 514800, -14086800, ...
[5] 0, 1, -2, 10, -90, 1248, -24240, 615600, -19378800, ...
[6] 0, 1, -2, 10, -90, 1248, -24360, 630720, -20719440, ...
[7] 0, 1, -2, 10, -90, 1248, -24360, 631440, -20860560, ...
[8] 0, 1, -2, 10, -90, 1248, -24360, 631440, -20865600, ...
MAPLE
a := n -> `if`(n=0, 0, (-1)^(n-1)*(n-1)!*add(Stirling2(n, i), i=0..n)):
seq(a(n), n=0..19);
# Alternatively use the function ExpLim defined in A320956.
ExpLim(19, x -> ln(x+1));
MATHEMATICA
a[n_] := If[n == 0, 0, (-1)^(n - 1)*(n - 1)!*Sum[StirlingS2[n, i], {i, 0, n}]]; Array[a, 19, 0] (* Amiram Eldar, Nov 07 2018 *)
PROG
(PARI) a(n) = if (n>0, (-1)^(n-1)*(n-1)!*sum(i=0, n, stirling(n, i, 2)), 0); \\ Michel Marcus, Nov 07 2018
CROSSREFS
Cf. A320956, A133942 (n=1), A000165 (n=2), A321398 (n=3).
Sequence in context: A377541 A277403 A179423 * A067550 A086587 A082472
KEYWORD
sign
AUTHOR
Peter Luschny, Nov 07 2018
STATUS
approved