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A009227
Expansion of e.g.f.: exp(sinh(x))/exp(x).
5
1, 0, 0, 1, 0, 1, 10, 1, 56, 281, 246, 4621, 16412, 53197, 564642, 1937937, 13309648, 100397649, 454215214, 4082253589, 26498068420, 174791970677, 1575851086778, 10628056916313, 91523101970104, 788580099169337, 6237722665351750, 60190551618214941
OFFSET
0,7
COMMENTS
Number of partitions of n-set in which block sizes are odd and greater than 1. - Vladeta Jovovic, Aug 23 2007
FORMULA
a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 09 2022
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, 2*j)*a(n-2*j-1), j=1..(n-1)/2))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Apr 09 2022
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[Sinh[x]]/Exp[x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 18 2015 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(sinh(x))/exp(x))) \\ Michel Marcus, Apr 09 2022
CROSSREFS
Sequence in context: A143471 A286921 A009209 * A305996 A030526 A327003
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Extended and signs tested by Olivier Gérard, Mar 15 1997
Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Jan 18 2015
STATUS
approved