A318124 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).

1, 1, 2, 9, 31, 127, 494, 1994, 8040, 32741, 133855, 549775, 2266756, 9372300, 38862245, 161500403, 672538548, 2805669061, 11723319333, 49055511943, 205534846202, 862167483656, 3620429584614, 15217780335870, 64022149180478, 269566679312520, 1135878674712355

Offset

0,3

Comments

For n > 2, a(n) is the n-th term of the weigh transform of n-gonal numbers.

Links

Table of n, a(n) for n=0..26.

N. J. A. Sloane, Transforms

Index to sequences related to polygonal numbers

Formula

a(n) ~ c * d^n / sqrt(n), where d = 4.2950655312028649462400... and c = 0.204576644650802181512... - Vaclav Kotesovec, Aug 19 2018

Mathematica

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}]

Crossrefs

Cf. A027998, A028377, A294102, A294836, A294837, A294838, A318118, A318125.

Sequence in context: A277245 A277246 A002774 * A295264 A150905 A150906

Adjacent sequences: A318121 A318122 A318123 * A318125 A318126 A318127

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 18 2018

Status

approved