A375363 - OEIS

%I #9 Aug 13 2024 11:39:31

%S 1,-1,5,1,19,30,102,242,666,1718,4555,11937,31435,82615,217301,571372,

%T 1502572,3951188,10390340,27322972,71850149,188941251,496850977,

%U 1306548125,3435774983,9034913514,23758733842,62477347430,164294064510,432037221810

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,4,10,10,5,1).

%F a(n) = -a(n-1) + 4*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).

%F a(n) = Sum_{k=0..n} binomial(3*k-2,n-k).

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

%o (PARI) a(n) = sum(k=0, n, binomial(3*k-2, n-k));

%Y Cf. A375362.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 13 2024