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 A155857 Row sums of triangle A155856. 4
 1, 2, 6, 23, 107, 590, 3786, 27821, 230869, 2137978, 21873854, 245151555, 2987967551, 39358156310, 557259550034, 8440866957273, 136211005966889, 2333068710452146, 42276699542130166, 808068680469402095 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For positive n, a(n) equals the permanent of the n X n matrix with 2's along the main diagonal and the upper diagonal, and 1's everywhere else. - John M. Campbell, Jul 09 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: 1/(1 -x -x/(1 -x -x/(1 -x -2*x/(1 -x -2*x/(1 -x -3*x/(1 -x -3*x/(1 - ... (continued fraction); a(n) = Sum_{k=0..n} binomial(2*n-k, k)*(n-k)!. a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*k!. - Paul Barry, May 28 2009 a(n) = (n+1)*a(n-1) -(n-3)*a(n-2) -a(n-3). - R. J. Mathar, Nov 15 2012 a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Feb 08 2014 MATHEMATICA Table[Sum[Binomial[2*n-k, k]*(n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *) PROG (Sage) [sum(binomial(2*n-k, k)*factorial(n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 05 2021 CROSSREFS Cf. A155856. Sequence in context: A071075 A007555 A101053 * A071076 A297196 A112501 Adjacent sequences: A155854 A155855 A155856 * A155858 A155859 A155860 KEYWORD nonn,easy AUTHOR Paul Barry, Jan 29 2009 STATUS approved

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Last modified December 9 17:12 EST 2022. Contains 358702 sequences. (Running on oeis4.)