A318125 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + (n - 3)*x^k)/(k*(1 - x^k)^4)).
1, 1, 3, 14, 54, 238, 1026, 4573, 20404, 91902, 415953, 1891908, 8638846, 39569655, 181766878, 836950153, 3861927937, 17853107055, 82668539290, 383360628369, 1780126898575, 8275908734103, 38517137597486, 179442212204245, 836741558761935, 3905012142470483
Offset: 0
Keywords
Links
- N. J. A. Sloane, Transforms
- Index to sequences related to pyramidal numbers
Programs
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Mathematica
Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k (1 + (n - 3) x^k)/(k (1 - x^k)^4), {k, 1, n}]], {x, 0, n}], {n, 0, 25}]
Formula
a(n) ~ c * d^n / sqrt(n), where d = 4.761510955746025663058811... and c = 0.2241869836397882024713... - Vaclav Kotesovec, Aug 19 2018
Comments