|
|
A348457
|
|
a(n) = Sum_{s=0..n} (-1)^s * ( Sum_{k=0..s} binomial(n,k) )^3.
|
|
2
|
|
|
1, -7, 38, -232, 1928, -16672, 133508, -1044736, 8337920, -67162624, 537953708, -4294193152, 34336008272, -274889261056, 2199555817952, -17592017354752, 140725278645248, -1125902437187584, 9007484455265852, -72057555801604096, 576453982622834768, -4611686599619510272, 36893651043755447672, -295147896302964047872
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
f := n -> add( (-1)^s*( add(binomial(n, k), k=0..s)^3 ), s=0..n);
[seq(f(n), n=0..50)];
|
|
MATHEMATICA
|
a[n_] := Sum[(-1)^m * Sum[Binomial[n, k], {k, 0, m}]^3, {m, 0, n}]; Array[a, 24, 0] (* Amiram Eldar, Oct 28 2021 *)
|
|
PROG
|
(PARI) a(n) = sum(s=0, n, (-1)^s*sum(k=0, s, binomial(n, k))^3); \\ Michel Marcus, Oct 28 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|