A369156 - OEIS

%I #12 Jan 15 2024 09:03:02

%S 1,4,22,140,968,7064,53544,417456,3326304,26967040,221733568,

%T 1844667136,15498804480,131325820032,1120928667264,9628975973120,

%U 83181462291968,722175844640768,6297942966129664,55143987250677760,484589284705202176,4272491458636754944

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4-x^4))/x)

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

%Y Cf. A107264, A369157.

%Y Cf. A317133, A369126.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 15 2024