A366119 - OEIS

%I #12 Oct 01 2023 10:37:26

%S 1,4,22,139,950,6831,50899,389402,3040433,24127641,194015198,

%T 1577355740,12943616840,107061667210,891666351501,7471125565836,

%U 62932782325745,532621542290355,4526846632642489,38621126867786485,330635368752515710,2839444812305017875

%N Expansion of (1/x) * Series_Reversion( x*(1+x+x^3)/(1+x)^5 ).

%H Seiichi Manyama, <a href="/A366119/b366119.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n+k,k) * binomial(4*n-k+4,n-3*k).

%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n+k, k)*binomial(4*n-k+4, n-3*k))/(n+1);

%Y Cf. A366116, A366117, A366118.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 29 2023