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Expansion of e.g.f. exp(Sum_{k=1..9} x^k).
2

%I #19 Feb 28 2024 10:46:26

%S 1,1,3,13,73,501,4051,37633,394353,4596553,55312291,744239541,

%T 10793656633,167689950013,2775839905203,48726598412521,

%U 903159189729121,17607070923233553,359702718305842243,7673827033741108573,171586828999546057641,3999150173195168500741

%N Expansion of e.g.f. exp(Sum_{k=1..9} x^k).

%H Seiichi Manyama, <a href="/A306624/b306624.txt">Table of n, a(n) for n = 0..465</a>

%F a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..min(9,n)} k*a(n-k)/(n-k)! for n > 0.

%t m=21; CoefficientList[Series[Exp[Sum[x^k, {k,1,9}]], {x, 0, m}], x] * Range[0,m]! (* _Amiram Eldar_, Mar 01 2019 *)

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, 9, x^k))))

%Y Column 9 of A293669.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 01 2019