OFFSET
3,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..500
M. Klazar, Bell numbers, their relatives and algebraic differential equations, J. Combin. Theory, A 102 (2003), 63-87.
FORMULA
G.f.: sum(x^k/[(1-x)(1-2x)...(1-kx)], k=3 (mod 4)). - Emeric Deutsch, Dec 15 2004
EXAMPLE
a(11)=92489 because stirling2(11,3)+stirling2(11,7)+stirling2(11,11)=92489.
MAPLE
seq(sum(stirling2(n, 3+4*k), k=0..(n-3)/4), n=3..26); # Emeric Deutsch, Dec 15 2004
# second Maple program:
with(combinat):
b:= proc(n, i, m) option remember; `if`(n=0, `if`(m=3, 1, 0),
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i-1, irem(m+j, 4)), j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=3..30); # Alois P. Heinz, Sep 17 2015
MATHEMATICA
Table[Sum[StirlingS2[n, 3+4*k], {k, 0, (n-3)/4}], {n, 3, 26}] (* Jean-François Alcover, Feb 18 2016, after Emeric Deutsch *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 12 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 15 2004
STATUS
approved