A375371 - OEIS

%I #10 Aug 13 2024 11:42:48

%S 1,-1,4,-1,11,7,35,52,138,267,606,1266,2758,5882,12679,27185,58442,

%T 125473,269561,578929,1243545,2670942,5736984,12322389,26467324,

%U 56849060,122106124,262271540,563332877,1209982051,2598919376,5582216323,11990037159,25753389147

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3,6,4,1).

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

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

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x*(1+x)^2)))

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

%Y Cf. A375373.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 13 2024