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A218219
Define a(x,y) to be 1 if x is 0 or 1 and y*a(x-1,y)-a(x-2,y) otherwise. Then the n-th term of the sequence is a(n,n).
1
1, 1, 1, 5, 41, 436, 5741, 90481, 1663585, 34988311, 828931049, 21851881930, 634556225161, 20129592507025, 692665874901013, 25699370092119569, 1022757988416562049, 43461563755791470416, 1964206882303435582865, 94076863910519354420761, 4760163616791818063701801
OFFSET
0,4
COMMENTS
The sequence grows about as fast as x!*e^x/p(x), where p(x) is a quadratic.
EXAMPLE
For 3, by definition, a(0,3)=1 and a(1,3)=1, so a(2,3)=3*a(1,3)-a(0,3)=3-1=2 and a(3,3)=3*a(2,3)-a(1,3)=6-1=5, so the third element is 5
CROSSREFS
Cf. A218220.
Sequence in context: A285064 A232685 A081215 * A140095 A259609 A323213
KEYWORD
nonn
AUTHOR
Nico Brown, Oct 23 2012
STATUS
approved