A361896 - OEIS

%I #11 Mar 30 2023 05:16:27

%S 1,3,30,300,3165,34584,386880,4400928,50692266,589584042,6910397886,

%T 81507086634,966408021984,11509174498254,137584249375308,

%U 1650109151463594,19847075122106145,239316542492974317,2892135259684291248,35021199836282568456,424837125616822551264

%N Expansion of 1/(1 - 9*x/(1 - x)^4)^(1/3).

%H Winston de Greef, <a href="/A361896/b361896.txt">Table of n, a(n) for n = 0..907</a>

%F a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n+3*k-1,n-k).

%F a(0) = 1; a(n) = (3/n) * Sum_{k=0..n-1} (n+2*k) * binomial(n+2-k,3) * a(k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x/(1-x)^4)^(1/3))

%Y Cf. A004987, A361375, A361843, A361844, A361845, A361880, A361895.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2023