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A173998
For n>=1, a(n) = n + 2 + sum(i=1..n-1, a(i)*a(n-i) ).
1
3, 13, 83, 673, 6203, 61613, 642683, 6940673, 76930803, 870136013, 10002590883, 116521027873, 1372486213803, 16318813519213, 195599588228683, 2360929398934273, 28671940652447203, 350089944825571213, 4295280755452388083, 52926654021145267873
OFFSET
1,1
COMMENTS
Using induction, it is easy to prove that a(n)==3 (mod 10).
The largest prime factors of these terms are large (they start 3, 13, 83, 673, 6203, 61613, 642683, 161411, 9221, 870136013, 751453, 4016443, 6267060337, 16318813519213,..)
LINKS
FORMULA
Recurrence: n*a(n) = 3*(5*n-7)*a(n-1) - (23*n-48)*a(n-2) + 9*(n-3)*a(n-3). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ sqrt(13*sqrt(10)-40)*(7+2*sqrt(10))^n/(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
aa=ConstantArray[0, 20]; aa[[1]]=3; Do[aa[[n]]=n+2+Sum[aa[[i]]*aa[[n-i]], {i, 1, n-1}], {n, 2, 20}]; aa (* Vaclav Kotesovec, Oct 20 2012 *)
CROSSREFS
Cf. A030431.
Sequence in context: A219906 A000904 A201304 * A135743 A123114 A104032
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Mar 05 2010
STATUS
approved