OFFSET
0,2
FORMULA
a(n) = Sum_{i=0..n} Sum_{k=0..n-i} Sum_{j=0..k} C(i,j)*C(j,k-j)*C(k+1,n-k-i)* C(k+i,i)/(k+1).
MAPLE
a:= n-> coeff(series(RootOf((A*x)^3+(A*x)^2+
A*(x-1)+x+1, A), x, n+1), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, May 14 2018
MATHEMATICA
Array[Sum[Sum[Sum[Binomial[i, j] Binomial[j, k - j], {j, 0, k}] Binomial[k + 1, # - k - i] Binomial[k + i, i]/(k + 1), {k, 0, # - i}], {i, 0, # + 1}] &, 31, 0] (* Michael De Vlieger, May 10 2018 *)
n = 27; A = Sum[a[k] x^k, {k, 0, n}] + x O[x]^n; Table[a[k], {k, 0, n}] /.
Solve[LogicalExpand[1 + x + x A + x^2 A^2 + x^3 A^3 == A]] // Flatten (* Peter Luschny, May 14 2018 *)
PROG
(Maxima)
a(n):=sum(sum(((sum(binomial(i, j)*binomial(j, k-j), j, 0, k))*binomial(k+1, n-k-i)* binomial(k+i, i))/(k+1), k, 0, n-i), i, 0, n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 07 2018
STATUS
approved