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G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^5.
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%I #8 Feb 21 2022 08:57:20

%S 1,-1,-4,-5,19,119,226,-789,-7747,-25333,29428,826059,4651651,7008499,

%T -108045466,-1124213961,-4968432059,6515205811,300350438716,

%U 2561696929271,9034737779711,-58377397309001,-1213955186657474,-9784487206914505,-27228229386096731,417997375131879519

%N G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^5.

%H Seiichi Manyama, <a href="/A346060/b346060.txt">Table of n, a(n) for n = 0..591</a>

%F a(n+1) = -Sum_{k=0..n} binomial(n+4,k+4) * a(k).

%t nmax = 25; A[_] = 0; Do[A[x_] = 1 - x A[x/(1 - x)]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%t a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n + 3, k + 4] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]

%Y Cf. A000587, A014619, A045500, A346053, A346059.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Jul 03 2021