OFFSET
0,2
FORMULA
a(n) = Sum_{i=0..n} binomial(n,i)*Sum_{j=0..i} binomial(i,j)^4.
From Vaclav Kotesovec, Oct 28 2019: (Start)
Recurrence: n^3*a(n) = (2*n - 1)*(8*n^2 - 8*n + 3)*a(n-1) + (n-1)*(22*n^2 - 44*n + 13)*a(n-2) - 44*(n-2)*(n-1)*(2*n - 3)*a(n-3) + 51*(n-3)*(n-2)*(n-1)*a(n-4).
a(n) ~ sqrt(2) * 17^(n + 3/2) / (64 * Pi^(3/2) * n^(3/2)). (End)
MATHEMATICA
Table[Sum[Binomial[n, i]*Sum[Binomial[i, j]^4, {j, 0, i}], {i, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2019 *)
PROG
(PARI) {a(n) = polcoef(polcoef(polcoef((1+(1+x)*(1+y)*(1+z)+(1+1/x)*(1+1/y)*(1+1/z))^n, 0), 0), 0)}
(PARI) {a(n) = sum(i=0, n, binomial(n, i)*sum(j=0, i, binomial(i, j)^4))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 28 2019
STATUS
approved