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Search: id:A001825
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| A001825 |
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Central factorial numbers.
(Formerly M5250 N2284)
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+0
5
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| 1, 35, 1974, 172810, 21967231, 3841278805, 886165820604, 261042753755556, 95668443268795341, 42707926241367380631, 22821422608929422854674, 14384681946935352617964750, 10562341153570752891930640875
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
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E.g.f.: (arcsin x)^5; that is, a_k is the coefficient of x^(2*k+5) in (arcsin x)^5 multiplied by (2*k+5)! and divided by 5! - Joe Keane (jgk(AT)jgk.org)
(-1)^(n-2)*a(n-2) is the coefficient of x^4 in prod(k=1, 2*n, x+2*k-2*n-1). - Benoit Cloitre and Michael Somos, Nov 22, 2002.
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EXAMPLE
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(arcsin x)^5 = x^5 + 5/6*x^7 + 47/72*x^9 + 1571/3024*x^11 + ...
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CROSSREFS
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Cf. A001824, A002455, A049033.
Right-hand column 3 in triangle A008956.
Adjacent sequences: A001822 A001823 A001824 this_sequence A001826 A001827 A001828
Sequence in context: A029560 A135923 A130005 this_sequence A094187 A115963 A025036
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Joe Keane (jgk(AT)jgk.org)
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