A370624 - OEIS

%I #12 May 01 2024 08:58:30

%S 1,1,3,13,55,231,987,4278,18711,82390,364793,1622556,7244419,32449158,

%T 145747290,656199048,2960596359,13382107227,60587421882,274712295550,

%U 1247233045905,5669390005950,25798654040580,117513750346200,535766200488675,2444698473079356

%N Coefficient of x^n in the expansion of 1 / (1-x-x^3)^n.

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

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

%Y Cf. A049140.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 01 2024