A369126 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4+x^4) ).
1, 4, 22, 140, 970, 7104, 54096, 424008, 3398224, 27721024, 229410328, 1921308272, 16253502512, 138683973120, 1192142838656, 10314377770720, 89749921081280, 784913791336192, 6895599255571840, 60825440855493376, 538507243041624864, 4783482648574893056
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- Index entries for reversions of series
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4+x^4))/x) -
PARI
a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(4*n-4*k+4, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(4*n-4*k+4,n-4*k).
D-finite with recurrence -3*(3*n+2)*(3*n+4)*(1746*n-6043)*(n+1)*a(n) +4*(519282*n^4 -1632448*n^3 +319539*n^2 +77803*n-72516)*a(n-1) +16*(-1055610*n^4 +5245655*n^3 -8423433*n^2 +5306215*n-1129842)*a(n-2) +96*(n-2) *(150552*n^3 -673240*n^2 +868987*n -301954)*a(n-3) -64*(n-2) *(n-3) *(174726*n^2 -528221*n +220460)*a(n-4) -512*(7353*n-3733)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Jan 24 2024