OFFSET
0,2
LINKS
Paul Barry and A. Hennessy, The Euler-Seidel Matrix, Hankel Matrices and Moment Sequences, J. Int. Seq. 13 (2010) # 10.8.2, Example 11.
FORMULA
a(n) = Sum_{i=0..n} binomial(n,i) * A000108(n+i).
D-finite with recurrence 2*n*(2*n+1)*(9*n-11)*a(n) +(-711*n^3+1589*n^2-986*n+144)*a(n-1) -10*(n-1)*(9*n-2)*(2*n-3)*a(n-2)=0.
MAPLE
MATHEMATICA
Table[Sum[Binomial[n, i] CatalanNumber[n + i], {i, 0, n}], {n, 0, 50}] (* Indranil Ghosh, Jul 20 2017 *)
PROG
(Python)
from sympy import binomial, catalan
def a(n): return sum(binomial(n, i)*catalan(n + i) for i in range(n + 1))
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 20 2017
(PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = sum(i=0, n, binomial(n, i) * C(n+i)); \\ Michel Marcus, Nov 12 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jul 20 2017
STATUS
approved