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 A063024 Reversion of y - y^2 - y^3 - y^4 - y^5. 0

%I #21 Apr 07 2019 19:03:56

%S 0,1,1,3,11,45,196,894,4215,20377,100463,503191,2553291,13097469,

%T 67808104,353851124,1859313324,9828998946,52237988523,278952216129,

%U 1495976545546,8053571710250,43507491045810,235784617161780

%N Reversion of y - y^2 - y^3 - y^4 - y^5.

%H Vladimir Kruchinin, <a href="http://arxiv.org/abs/1211.3244">The method for obtaining expressions for coefficients of reverse generating functions</a>, arXiv:1211.3244 [math.CO], 2012.

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

%F a(n)=sum(k=1..n-1, (sum(j=0..k, binomial(k,j)*sum(i=j..n-k+j-1, binomial(j,i-j)*binomial(k-j,n-3*(k-j)-i-1))))*binomial(n+k-1,n-1)/n, n>1. a(1)=1. [_Vladimir Kruchinin_, May 10 2011]

%t CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^4 - y^5, {y, 0, 30}], x], x]

%o (Maxima)

%o a(n):=if n<2 then n else sum((sum(binomial(k,j)*sum(binomial(j,i-j)*binomial(k-j,n-3*(k-j)-i-1),i,j,n-k+j-1),j,0,k))*binomial(n+k-1,n-1),k,1,n-1)/n; /* _Vladimir Kruchinin_, May 10 2011 */

%o (PARI)

%o x='x+O('x^66);

%o gf=serreverse(x-sum(j=2, 6, x^j));

%o Vec(gf)

%o /* _Joerg Arndt_, May 12 2011 */

%K nonn,easy

%O 0,4

%A _Olivier GĂ©rard_, Jul 05 2001

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Last modified March 1 08:46 EST 2024. Contains 370430 sequences. (Running on oeis4.)