A369514 - OEIS

%I #8 Jan 25 2024 07:51:07

%S 1,6,57,652,8250,111228,1566384,22770990,339136149,5147965790,

%T 79355002155,1238845925070,19546811164017,311215082863152,

%U 4993737492276384,80673666233512572,1311052196736963738,21418709030787603984,351563022864652061086,5794815410347964694408

%N Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^3)^2 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(7*n+5,n-3*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^3)^2)/x)

%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n+k+1, k)*binomial(7*n+5, n-3*k))/(n+1);

%Y Cf. A369114.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 25 2024