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a(n) = [x^n] (5040 / Sum_{k=0..n} (k+7)!*x^k)^(1/4).
3

%I #11 Apr 29 2018 13:00:20

%S 1,-2,-8,-60,-600,-7152,-96456,-1430544,-22933920,-393013280,

%T -7144207808,-137001926144,-2760226854816,-58242464679360,

%U -1283886660610560,-29506641823939200,-705788634473952000,-17544801385483584000,-452659831142363014400

%N a(n) = [x^n] (5040 / Sum_{k=0..n} (k+7)!*x^k)^(1/4).

%H Seiichi Manyama, <a href="/A303672/b303672.txt">Table of n, a(n) for n = 0..444</a>

%p [seq(coeff(series((factorial(7)/add(factorial(k+7)*x^k,k=0..n))^(1/4), x,30),x,n),n=0..25)]; # _Muniru A Asiru_, Apr 29 2018

%o (PARI) N=66; x='x+O('x^N); Vec((7!/sum(k=0, N, (k+7)!*x^k))^(1/4))

%Y Cf. A077607, A303671, A303673.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 28 2018