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A348064
Coefficient of x^3 in expansion of n!* Sum_{k=0..n} binomial(x,k).
5
1, -2, 25, -75, 1099, -4340, 79064, -382060, 8550916, -48306984, 1303568760, -8346754416, 266955481584, -1894529909376, 70785236377728, -547468189825536, 23610353987137536, -196402650598402560, 9679304091074250240, -85687212859582878720, 4785340778000524477440
OFFSET
3,2
FORMULA
E.g.f.: (log(1 + x))^3/(6 * (1 - x)).
PROG
(PARI) a(n) = n!*polcoef(sum(k=3, n, binomial(x, k)), 3);
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(log(1+x)^3/(6*(1-x))))
(Python)
from sympy.abc import x
from sympy import ff, expand
def A348064(n): return sum(ff(n, n-k)*expand(ff(x, k)).coeff(x**3) for k in range(3, n+1)) # Chai Wah Wu, Sep 27 2021
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 26 2021
STATUS
approved