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A348068
Coefficient of x^5 in expansion of n!* Sum_{k=0..n} binomial(x,k).
5
1, -9, 112, -1064, 12873, -140595, 1870385, -23551110, 351042406, -5043110072, 84074954600, -1361614072000, 25218570009424, -455365645674480, 9298765013106384, -185409487083100320, 4144212593899945056, -90492302454898284864, 2199399908894486591040
OFFSET
5,2
FORMULA
E.g.f.: (log(1 + x))^5/(120 * (1 - x)).
PROG
(PARI) a(n) = n!*polcoef(sum(k=5, n, binomial(x, k)), 5);
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(log(1+x)^5/(120*(1-x))))
(Python)
from sympy.abc import x
from sympy import ff, expand
def A348068(n): return sum(ff(n, n-k)*expand(ff(x, k)).coeff(x**5) for k in range(5, n+1)) # Chai Wah Wu, Sep 27 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 27 2021
STATUS
approved