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 A002019 a(n)=a(n-1)-(n-1)(n-2)a(n-2). (Formerly M4330 N1813) 8
 1, 1, 1, -1, -7, 5, 145, -5, -6095, -5815, 433025, 956375, -46676375, -172917875, 7108596625, 38579649875, -1454225641375, -10713341611375, 384836032842625, 3663118565923375, -127950804666254375, -1519935859717136875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES Dwight, Tables of Integrals ..., Eq. 552.5, page 133. R. Kelisky, The numbers generated by exp(arctan x), Duke Math. J., 26 (1959), 569-581. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=0..100 Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 FORMULA E.g.f.: exp(arctan(x)). a(n)=n!*sum(if oddp(m+n) then 0 else (-1)^((3*n+m)/2)/(2^m*m!)*sum(2^i*binomial(n-1,i-1)*m!/i!*stirling1(i,m),i,m,n),m,1,n), n>0. [From Vladimir Kruchinin, Aug 05 2010] E.g.f.: exp(arctan(x))=1+2x/(H(0)-x); H(k)=4k+2+x^2*(4k^2+8k+5)/H(k+1); (continued fraction). - Sergei N. Gladkovskii, Nov 15 2011 a(n+1) = a(n) - a(n-1) * A002378(n-2). [Reinhard Zumkeller, Feb 27 2012] MAPLE a(n):=n!*sum(if oddp(m+n) then 0 else (-1)^((3*n+m)/2)/(2^m*m!)*sum(2^i*binomial(n-1, i-1)*m!/i!*stirling1(i, m), i, m, n), m, 1, n); (for Maxima) [From Vladimir Kruchinin, Aug 05 2010] MATHEMATICA RecurrenceTable[{a[0]==1, a[1]==1, a[n]==a[n-1]-(n-1)(n-2)a[n-2]}, a[n], {n, 30}] (* From Harvey P. Dale, May 02 2011 *) PROG (Haskell) a002019 n = a002019_list !! n a002019_list = 1 : 1 : zipWith (-)    (tail a002019_list) (zipWith (*) a002019_list a002378_list) -- Reinhard Zumkeller, Feb 27 2012 CROSSREFS Bisections are A102058 and A102059. Cf. A006228. Row sums of signed triangle A049218. Cf. A000246. Sequence in context: A005692 A080798 A007553 * A012878 A003299 A198677 Adjacent sequences:  A002016 A002017 A002018 * A002020 A002021 A002022 KEYWORD sign,nice,easy AUTHOR EXTENSIONS More terms from H. P. Robinson. STATUS approved

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