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A002019
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a(n)=a(n-1)-(n-1)(n-2)a(n-2).
(Formerly M4330 N1813)
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7
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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; internal format)
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OFFSET
| 0,5
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
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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 Kruchinin Vladimir (kru(AT)ie.tusur.ru), 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
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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 Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 05 2010]
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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 *)
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CROSSREFS
| Bisections are A102058 and A102059.
Cf. A006228.
Row sums of signed triangle A049218.
Sequence in context: A005692 A080798 A007553 * A012878 A003299 A198677
Adjacent sequences: A002016 A002017 A002018 * A002020 A002021 A002022
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KEYWORD
| sign,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from H. P. Robinson.
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