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Coefficient of x^4 in expansion of n!* Sum_{k=0..n} binomial(x,k).
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%I #18 Sep 27 2021 18:31:47

%S 1,-5,55,-350,3969,-31563,408050,-3920950,58206676,-657328100,

%T 11111159696,-144321864960,2747845864464,-40364369180016,

%U 856755330487200,-14042902728462624,329258021171239296,-5956512800554963584,153050034289602269952,-3028534064042216488704,84691080748928315003904

%N Coefficient of x^4 in expansion of n!* Sum_{k=0..n} binomial(x,k).

%F E.g.f.: (log(1 + x))^4/(24 * (1 - x)).

%o (PARI) a(n) = n!*polcoef(sum(k=4, n, binomial(x, k)), 4);

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(log(1+x)^4/(24*(1-x))))

%o (Python)

%o from sympy.abc import x

%o from sympy import ff, expand

%o def A348065(n): return sum(ff(n,n-k)*expand(ff(x,k)).coeff(x**4) for k in range(4,n+1)) # _Chai Wah Wu_, Sep 27 2021

%Y Column k=4 of A190782.

%Y Cf. A000482, A054651, A028341, A347987, A348063, A348064, A348068.

%K sign

%O 4,2

%A _Seiichi Manyama_, Sep 26 2021