A370280 - OEIS

%I #7 Feb 14 2024 10:48:20

%S 1,3,25,234,2305,23373,241486,2527920,26720529,284555700,3048323135,

%T 32812937820,354619072990,3845377105794,41817926091120,

%U 455893204069944,4980851709418353,54521955043418925,597823622561048020,6564929893462467450,72189820135528858455

%N Coefficient of x^n in the expansion of 1/( (1-x)^2 - x )^n.

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

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * ((1-x)^2 - x) ).

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(3*n+k-1, n-k));

%Y Cf. A069723, A370282.

%Y Cf. A249924.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024