A371341 G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^5).
1, 2, 6, 46, 330, 2778, 24094, 219318, 2048274, 19583410, 190497142, 1880184446, 18778814938, 189456108554, 1927852050830, 19763367194630, 203919590002210, 2116079501498722, 22069907395614182, 231222485352688590, 2432325883912444010
Offset: 0
Keywords
Programs
-
Maple
A371341 := proc(n) if n = 0 then 1; else add(binomial(n,k)*binomial(2*n-5*k-2,n-1),k=0..n) ; (-1)^(n-1)*%/n ; end if; end proc: seq(A371341(n),n=0..60) ; # R. J. Mathar, Apr 22 2024
-
PARI
a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-5*k-2, n-1))/n);
Formula
a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-5*k-2,n-1) for n > 0.