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A049033 Central factorial numbers. 4

%I #8 Feb 22 2015 18:42:40

%S 1,56,4368,489280,75851776,15658639360,4165906530304,1390437378293760,

%T 569462999991975936,280969831084430721024,164441704270786486861824,

%U 112668650067303149573505024

%N Central factorial numbers.

%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

%F 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)

%F (-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

%e (arcsin x)^6 = x^6 + x^8 + 13/15*x^10 + 139/189*x^12 + ...

%Y Cf. A001824, A001825, A002455.

%Y Equals 4^n * A001820(n).

%K nonn

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)

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Last modified April 23 12:08 EDT 2024. Contains 371912 sequences. (Running on oeis4.)