A030274 Numerators of sequence {b(1), b(2), ...} which when COMPOSED with itself gives {1,2,3,...}.
1, 1, 1, 1, 1, 0, 1, 3, -29, 25, 263, -1481, -5493, 80505, 41549, -10584341, 14534299, 431101045, -1767586509, -43076199745, 322525095431, 1295531336537, -30908646610497, -734222129667169, 13259294064756895, 59705027567272273, -1617292893727823431, -1346735121534484263
Offset: 1
Examples
1, 1, 1/2, 1/4, 1/8, 0, 1/16, 3/64, -29/128, 25/128, 263/256, -1481/512, -5493/1024, 80505/2048, ... = A030274/A030275
Links
- Dmitry Kruchinin and Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986 [math.CO], 2013.
- N. J. A. Sloane, Transforms
Programs
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Mathematica
t[n_, m_] := t[n, m] = If[ n == m , 1 , 1/2*(Binomial[n+m-1, 2*m-1] - Sum[t[n, i]*t[i, m], {i, m+1, n-1}])]; a[n_] := t[n, 1] // Numerator; Table[a[n], {n, 1, 28}] (* Jean-François Alcover, Feb 26 2013, after Vladimir Kruchinin *) -
Maxima
T(n, m):=if n=m then 1 else 1/2*(binomial(n+m-1, 2*m-1)-sum(T(n, i)*T(i, m), i, m+1, n-1)); makelist(num(T(n, 1)), n, 1, 10); /* Vladimir Kruchinin, Mar 14 2012 */
Formula
a(n) = numerator(T(n,1)), T(n,m) = (1/2)*(binomial(n+m-1,2*m-1) - sum(i=m+1..n-1, T(n,i)*T(i,m))), n > m, T(n,n)=1. - Vladimir Kruchinin, Mar 14 2012
Extensions
More terms from Vladeta Jovovic, Dec 19 2003