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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 (list; graph; refs; listen; history; text; internal format)
 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 Vincenzo Librandi, Table of n, a(n) for n = 1..200 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 Adjacent sequences:  A173995 A173996 A173997 * A173999 A174000 A174001 KEYWORD nonn AUTHOR Vladimir Shevelev, Mar 05 2010 STATUS approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)