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A189924 a(n) = abs(Stirling1(n+2,2)) - abs(Stirling1(n+2,3)). 2
1, 2, 5, 15, 49, 140, -64, -8540, -146124, -2124936, -30374136, -445116672, -6793958016, -108691150464, -1826654613120, -32257962443520, -598196854045440, -11635261535301120, -237044583523514880, -5050811716879104000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
This is the fourth (k=3) column sequence in triangle A094645 without leading zeros.
LINKS
FORMULA
a(n) = abs(Stirling1(n+2,2)) - abs(Stirling1(n+2,3)), with the unsigned Stirling1 numbers abs(Stirling1(n,k)) = A132393(n,k).
E.g.f.: (1/2)*(2-log(1-x)^2)/(1-x)^2 (from differentiating three times (1-x)*((-log(1-x))^3)/3!).
MATHEMATICA
Table[Abs[StirlingS1[n+2, 2]]-Abs[StirlingS1[n+2, 3]], {n, 0, 20}] (* Harvey P. Dale, May 21 2015 *)
PROG
(PARI) a(n)=abs(stirling(n+2, 2))-abs(stirling(n+2, 3)) \\ Charles R Greathouse IV, Jun 27 2011
(Magma) [Abs(StirlingFirst(n+2, 2)) - Abs(StirlingFirst(n+2, 3)): n in [0..30]]; // G. C. Greubel, Jan 13 2018
CROSSREFS
Cf. A081047 (column k=2).
Sequence in context: A149929 A337262 A149930 * A360233 A190908 A149931
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Jun 21 2011
STATUS
approved

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Last modified June 17 11:50 EDT 2024. Contains 373445 sequences. (Running on oeis4.)