A049033 Central factorial numbers.

1, 56, 4368, 489280, 75851776, 15658639360, 4165906530304, 1390437378293760, 569462999991975936, 280969831084430721024, 164441704270786486861824, 112668650067303149573505024

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