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Expansion of (1/x) * Series_Reversion( x*(1-x-x^5)/(1-x) ).
2

%I #17 Sep 24 2024 14:14:42

%S 1,0,0,0,0,1,1,1,1,1,7,14,22,31,41,103,235,457,791,1261,2399,5015,

%T 10257,19676,35296,65170,127520,256187,507601,969495,1834433,3534477,

%U 6962249,13809538,27061252,52439361,101701035,199152071,393332277,776589611,1525416837

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

%H Seiichi Manyama, <a href="/A366112/b366112.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} binomial(n+k,k) * binomial(n-4*k-1,n-5*k).

%o (PARI) a(n) = sum(k=0, n\5, binomial(n+k, k)*binomial(n-4*k-1, n-5*k))/(n+1);

%Y Cf. A046736, A054514, A215342.

%Y Cf. A017899.

%K nonn

%O 0,11

%A _Seiichi Manyama_, Sep 29 2023