A348064 Coefficient of x^3 in expansion of n!* Sum_{k=0..n} binomial(x,k).

1, -2, 25, -75, 1099, -4340, 79064, -382060, 8550916, -48306984, 1303568760, -8346754416, 266955481584, -1894529909376, 70785236377728, -547468189825536, 23610353987137536, -196402650598402560, 9679304091074250240, -85687212859582878720, 4785340778000524477440

Offset

3,2

Links

Table of n, a(n) for n=3..23.

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

Column k=3 of A190782.

Cf. A000399, A000454, A054651, A081051, A028340, A347987, A348063, A348065, A348068.

Sequence in context: A153478 A226491 A062933 * A069232 A269232 A181920

Adjacent sequences: A348061 A348062 A348063 * A348065 A348066 A348067

Keyword

sign

Author

Seiichi Manyama, Sep 26 2021

Status

approved