A335647 - OEIS

%I #12 Jun 24 2020 03:15:42

%S 1,10,84,715,6188,54264,480700,4292145,38567100,348330136,3159461968,

%T 28760021745,262596783764,2403979904200,22057981462440,

%U 202802465047245,1867897112363100,17231414395464984,159186450151978480,1472474663905800940,13636219405675529520

%N a(n) = binomial(4*n+1,n+1).

%F G.f. A(x)=x*B'(x)/B(x)+x*(1/x-1/(B(x))', B(x)=x(1+B(x))^4.

%F a(n) = Sum_{k=0..n+1} C(n+1,k)*C(3*n,k).

%o (Maxima)

%o a(n):=sum(binomial(n+1,k)*binomial(3*n,k),k,0,n+1);

%o (PARI) a(n) = binomial(4*n+1, n+1); \\ _Michel Marcus_, Jun 15 2020

%Y Cf. A002293.

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Jun 15 2020