A365692 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^2*A(x)^4).
1, 1, 1, 2, 7, 23, 72, 238, 831, 2959, 10645, 38824, 143492, 535700, 2016020, 7641574, 29152015, 111841263, 431209723, 1669945778, 6493144143, 25338440143, 99204579648, 389570145288, 1534026813892, 6055885764548, 23962654178012, 95023123291680
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(n+2*k+1, n-2*k)/(n+2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(n+2*k+1,n-2*k) / (n+2*k+1).