A370282 - OEIS

%I #7 Feb 14 2024 10:48:11

%S 1,4,42,499,6250,80634,1060269,14127852,190102482,2577310285,

%T 35150819132,481734467955,6628611532621,91517611501008,

%U 1267182734325900,17589579427715124,244689432718144770,3410399867585709501,47613678409439712861,665756829352248572725

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

%F a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(4*n+2*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)^3 - x) ). See A369215.

%o (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(4*n+2*k-1, n-k));

%Y Cf. A069723, A370280.

%Y Cf. A369215.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024