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A049033 Central factorial numbers. 4
1, 56, 4368, 489280, 75851776, 15658639360, 4165906530304, 1390437378293760, 569462999991975936, 280969831084430721024, 164441704270786486861824, 112668650067303149573505024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..11.

FORMULA

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

EXAMPLE

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

CROSSREFS

Cf. A001824, A001825, A002455.

Equals 4^n * A001820(n).

Sequence in context: A239816 A220108 A003747 * A271138 A271139 A271140

Adjacent sequences:  A049030 A049031 A049032 * A049034 A049035 A049036

KEYWORD

nonn

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.