A335647 a(n) = binomial(4*n+1,n+1).

1, 10, 84, 715, 6188, 54264, 480700, 4292145, 38567100, 348330136, 3159461968, 28760021745, 262596783764, 2403979904200, 22057981462440, 202802465047245, 1867897112363100, 17231414395464984, 159186450151978480, 1472474663905800940, 13636219405675529520

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

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

Prog

(Maxima)
a(n):=sum(binomial(n+1, k)*binomial(3*n, k), k, 0, n+1);
(PARI) a(n) = binomial(4*n+1, n+1); \\ Michel Marcus, Jun 15 2020

Crossrefs

Cf. A002293.

Sequence in context: A016131 A027310 A287826 * A364416 A155593 A239990

Adjacent sequences: A335644 A335645 A335646 * A335648 A335649 A335650

Keyword

nonn

Author

Vladimir Kruchinin, Jun 15 2020

Status

approved