OFFSET
0,2
FORMULA
a(n) = Sum_{i=0..n} binomial(n,i)*Sum_{j=0..i} binomial(i,j)^5.
From Vaclav Kotesovec, Oct 28 2019: (Start)
Recurrence: n^4*(40*n^2 - 24*n - 79)*a(n) = (1080*n^6 - 2808*n^5 + 875*n^4 + 2928*n^3 - 3762*n^2 + 1834*n - 336)*a(n-1) + (9320*n^6 - 42872*n^5 + 61193*n^4 - 12152*n^3 - 35518*n^2 + 21658*n - 2016)*a(n-2) - (n-2)*(48560*n^5 - 223376*n^4 + 216118*n^3 + 381866*n^2 - 791133*n + 355194)*a(n-3) + (n-3)*(n-2)*(79560*n^4 - 286416*n^3 - 56675*n^2 + 976675*n - 616322)*a(n-4) - 11*(n-4)*(n-3)*(n-2)*(5080*n^3 - 8128*n^2 - 25641*n + 21693)*a(n-5) + 363*(n-5)*(n-4)*(n-3)*(n-2)*(40*n^2 + 56*n - 63)*a(n-6).
a(n) ~ 33^(n+2) / (256 * sqrt(5) * Pi^2 * n^2). (End)
MATHEMATICA
Table[Sum[Binomial[n, i]*Sum[Binomial[i, j]^5, {j, 0, i}], {i, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2019 *)
PROG
(PARI) {a(n) = sum(i=0, n, binomial(n, i)*sum(j=0, i, binomial(i, j)^5))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 28 2019
STATUS
approved