A369024 - OEIS

%I #21 Jan 25 2024 11:16:30

%S 1,7,81,1135,17617,291479,5038177,89901023,1643514849,30623478951,

%T 579444828465,11103818394447,215053322179121,4202849976054583,

%U 82778942956393409,1641477474636943295,32743892109730116801,656612555241354578759,13228883898856161274129

%N Expansion of (1/x) * Series_Reversion( x * (1-2*x)^4 / (1-x) ).

%H Seiichi Manyama, <a href="/A369024/b369024.txt">Table of n, a(n) for n = 0..749</a>

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

%F a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(4*n+2,n-k).

%F D-finite with recurrence -2*(462919*n-251445)*(4*n+1) *(2*n+1)*(4*n+3) *(n+1)*a(n) +(625365036*n^5 +403579400*n^4 -437229300*n^3 +49132810*n^2 -20878971*n +3771675)*a(n-1) +(484851248*n^5 -3077382030*n^4 +7964893000*n^3 -10232074140*n^2 +6398384592*n -1533654945)*a(n-2) +(652184*n-451475)*(4*n-9) *(n-2)*(4*n-7)*(2*n-3)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2024

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^4/(1-x))/x)

%o (PARI) a(n, s=1, t=4, u=-1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

%Y Cf. A344553, A369023.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 12 2024