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Search: id:A049033
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| A049033 |
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Central factorial numbers. |
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+0
5
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| 1, 56, 4368, 489280, 75851776, 15658639360, 4165906530304, 1390437378293760, 569462999991975936, 280969831084430721024, 164441704270786486861824, 112668650067303149573505024
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
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FORMULA
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E.g.f.: (arcsin x)^6; that is, a_k is the coefficient of x^(2*k+6) in (arcsin x)^6 multiplied by (2*k+6)! and divided by 6! - Joe Keane (jgk(AT)jgk.org)
(-1)^(n-2)*a(n-2) is the coefficient of x^5 in prod(k=0, 2*n, x+2*k-2*n). - Benoit Cloitre and Michael Somos, Nov 22, 2002.
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EXAMPLE
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(arcsin x)^6 = x^6 + x^8 + 13/15*x^10 + 139/189*x^12 + ...
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CROSSREFS
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Cf. A001824, A001825, A002455.
Equals 4^n * A001820(n).
Sequence in context: A003696 A042513 A003747 this_sequence A009600 A082167 A006690
Adjacent sequences: A049030 A049031 A049032 this_sequence A049034 A049035 A049036
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KEYWORD
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nonn
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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