OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1233 (terms n = 1..200 from Vincenzo Librandi)
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = sum(k=0..n-1, binomial(k+n,n-k-1)*sum(j=0..n, binomial(n,j)*binomial(j,k-2*n+2*j)))/n, n>0.
MAPLE
a:= n-> coeff(series(RootOf(x*(((((A+3)*A+4)*
A+3)*A+2)*A+1)-A, A), x, n+1), x, n):
seq(a(n), n=0..25); # Alois P. Heinz, Jul 22 2018
MATHEMATICA
terms = 25;
A[_] = 1; Do[A[x_] = x*(A[x]^5 + 3A[x]^4 + 4A[x]^3 + 3A[x]^2 + 2A[x] + 1) + O[x]^(terms+1), {terms+1}];
CoefficientList[A[x], x] // Rest (* Jean-François Alcover, Jul 22 2018 *)
PROG
(PARI)
a(n)=sum(k=0, n, binomial(k+n+1, n-k)*sum(j=0, n+1, binomial(n+1, j)*binomial(j, k-2*n-2+2*j)))/(n+1);
vector(33, n, a(n-1)) /* show terms, Joerg Arndt, Mar 04 2011 */
(Magma) [&+[Binomial(k+n, n-k-1)*(Binomial(n, i)*Binomial(i, k-2*n+2*i))/n: k in [0..25], i in [0..n]]: n in [1..25]]; // Vincenzo Librandi, Jul 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 28 2011
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, Jul 23 2018
STATUS
approved