A392641 - OEIS

A392641

Expansion of 1 / sqrt((1-x)^6 - 4*x).

1, 5, 30, 210, 1555, 11853, 92082, 724950, 5763795, 46172855, 372102306, 3013333458, 24500724241, 199885491275, 1635455540700, 13414669956880, 110272326857385, 908207029425765, 7492741133150170, 61909184062082850, 512225173969783845, 4243273059425952495

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n+5*k+2,n-k).

MATHEMATICA

Table[Sum[Binomial[2*k, k]*Binomial[n+5*k+2, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Jan 19 2026 *)

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x)^6-4*x))

(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R! 1 / Sqrt((1-x)^6 - 4*x)); // Vincenzo Librandi, Jan 19 2026