A318118 a(n) = [x^n] exp(Sum_{k>=1} x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^3)).

1, 1, 3, 10, 40, 150, 616, 2456, 10102, 41400, 171526, 712111, 2972115, 12434993, 52195414, 219567909, 925704792, 3909841659, 16541598215, 70085877919, 297347922785, 1263046810334, 5370930049915, 22861883482838, 97402827429118, 415332438952517, 1772380322197432

Offset: 0

Author

Ilya Gutkovskiy, Aug 18 2018

Keywords

• nonn

Comments

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000294, A023871, A274998, A278767, A278768, A278769.

Programs

Mathematica

Table[SeriesCoefficient[Exp[Sum[x^k (1 + (n - 3) x^k)/(k (1 - x^k)^3), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]

Formula

a(n) ~ c * d^n / sqrt(n), where d = 4.3505530790182509701639869563721679988879373943131559534408716195123... and c = 0.2276354216252041005336767937139336687746108521151301186102034... - Vaclav Kotesovec, Aug 18 2018