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%I #6 Aug 19 2018 07:25:02
%S 1,1,2,9,31,127,494,1994,8040,32741,133855,549775,2266756,9372300,
%T 38862245,161500403,672538548,2805669061,11723319333,49055511943,
%U 205534846202,862167483656,3620429584614,15217780335870,64022149180478,269566679312520,1135878674712355
%N a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).
%C For n > 2, a(n) is the n-th term of the weigh transform of n-gonal numbers.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F a(n) ~ c * d^n / sqrt(n), where d = 4.2950655312028649462400... and c = 0.204576644650802181512... - _Vaclav Kotesovec_, Aug 19 2018
%t Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k (1 + (n - 3) x^k)/(k (1 - x^k)^3), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]
%Y Cf. A027998, A028377, A294102, A294836, A294837, A294838, A318118, A318125.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 18 2018