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A305209 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - n*x^k))). 1

%I #5 May 27 2018 19:47:14

%S 1,1,2,12,86,885,11234,172711,3112262,64422126,1506406702,39279802969,

%T 1130133725736,35566642690293,1215444767739120,44823725114186355,

%U 1774344335649148230,75042087586212893216,3377041177800135323864,161125608740713509132809,8124438293071792011560256

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

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) = [x^n] Product_{k>=1} (1 + x^k)^(n^(k-1)).

%t Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k/(k (1 - n x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 20}]

%t Table[SeriesCoefficient[Product[(1 + x^k)^(n^(k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

%Y Cf. A098407, A292805, A305207.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 27 2018

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Last modified March 29 02:15 EDT 2024. Contains 371264 sequences. (Running on oeis4.)