OFFSET
0,3
COMMENTS
Row sums of Eulerian triangle A008292 yield the factorials.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..253
FORMULA
a(n) = Sum_{k=0..n} [ Sum_{j=0..k} (-1)^j*(k-j)^n*C(n+1, j) ]^2.
EXAMPLE
a(1) = 1 = 1;
a(2) = 1 + 1 = 2;
a(3) = 1 + 4^2 + 1 = 18;
a(4) = 1 + 11^2 + 11^2 + 1 = 244;
a(5) = 1 + 26^2 + 66^2 + 26^2 + 1 = 5710;
a(6) = 1 + 57^2 + 302^2 + 302^2 + 57^2 + 1 = 188908.
MAPLE
a:= n-> add(combinat[eulerian1](n, k)^2, k=0..n):
seq(a(n), n=0..18); # Alois P. Heinz, Sep 10 2020
PROG
(PARI) {a(n)=sum(k=0, n, sum(j=0, k, (-1)^j*(k-j)^n*binomial(n+1, j))^2)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 29 2009
STATUS
approved