A365754 - OEIS

%I #15 Feb 17 2024 02:39:51

%S 1,5,36,305,2833,27916,286632,3033513,32858595,362515725,4059475368,

%T 46021411644,527163783916,6092053249160,70939443268112,

%U 831558454663449,9804617762941095,116201796106426543,1383557994261012100,16541672701743657545,198510770031798279825

%N Expansion of  (1/x) * Series_Reversion( x*(1-x)/(1+x)^4 ).

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

%F a(n) = (1/(n+1)) * [x^n] ( (1+x)^4 / (1-x) )^(n+1). - _Seiichi Manyama_, Feb 17 2024

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

%Y Cf. A000108, A006318, A107111, A263843, A365755.

%Y Cf. A365752.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 18 2023