OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k) * multinomial(k,k,k)/(k+1).
a(n) = hypergeometric(1/3,2/3,-n; 1,2; -27).
a(n) == 1 (mod 3) for all natural n.
E.g.f.: exp(t) * hypergeometric(1/3,2/3; 1,2; 27*t).
From Vaclav Kotesovec, Oct 26 2016: (Start)
Recurrence: n*(n+1)*a(n) = 2*(3*n-1)*(5*n-3)*a(n-1) - (n-1)*(57*n-56)*a(n-2) + 28*(n-2)*(n-1)*a(n-3).
a(n) ~ 2^(2*n+3) * 7^(n+2) / (3^(11/2) * Pi * n^2).
(End)
Diff. eq. satisfied by the ordinary g.f.: t*(1-t)^2*(1-28*t)*A''(t)+2*(1-t)*(1-2*t)*(1-28*t)*A'(t)-2*(4-29*t+28*t^2)*A(t)=0. - Emanuele Munarini, Oct 28 2016
MATHEMATICA
Table[Sum[Binomial[n, k] Multinomial[k, k, k]/(k+1), {k, 0, n}], {n, 0, 100}]
PROG
(Maxima) makelist(sum(binomial(n, k)*multinomial_coeff(k, k, k)/(k+1), k, 0, n), n, 0, 12);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 25 2016
STATUS
approved