A381876 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.
1, 4, 23, 156, 1167, 9311, 77710, 670294, 5928183, 53467931, 489904745, 4547296624, 42667426369, 404044679434, 3856480309376, 37062228265769, 358330619946164, 3482936427997599, 34014454418349579, 333598711996924548, 3284326412065118717, 32446900771699499147
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+2, n-k)/(n+k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+k+1,k) * binomial(4*n-4*k+2,n-k)/(n+k+1).
a(n) = binomial(2 + 4*n, n)*hypergeom([-2/3-n, -1/3-n, -n, 1+n], [-1/2-n, -1/4-n, 1/4-n], 3^3/2^8)/(1 + n). - Stefano Spezia, Mar 09 2025