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G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^5.
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%I #14 Mar 26 2024 11:14:57

%S 1,5,45,470,5375,65231,825225,10764185,143739440,1955340360,

%T 27001732972,377530388235,5333865386885,76031188364860,

%U 1092117166466660,15792298241897649,229704197116753825,3358528175751886765,49333470827844265285,727680248026484478405

%N G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^5.

%F a(n) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+4,k)/(k+1).

%F G.f.: A(x) = B(x/(1-x)), where B(x) = (1/x) * Series_Reversion( x*(1-x)^5 ).

%F G.f.: A(x) = B(x)^5 where B(x) is the g.f. of A349333.

%o (PARI) a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));

%Y Cf. A349333, A371379, A371521, A371522, A371523.

%Y Cf. A270386, A371483, A371486.

%Y Cf. A130564.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024