A027436
G.f. f(x) = Sum_{n>=1} a(n)*x^n satisfies f(f(x)) = x*(1 + 4*x).
Original entry on oeis.org
0, 1, 2, -4, 16, -80, 432, -2304, 10944, -35328, -74112, 2736384, -30853632, 238663680, -1247457280, 2201247744, 32530722816, -320650199040, 156266184704, 18314630348800, -20667999748096, -3428200020508672
Offset: 0
A097088
Numerators of coefficients in function A(x) such that A(A(x)) = x+x^2.
Original entry on oeis.org
0, 1, 1, -1, 1, -5, 27, -9, 171, -69, -579, 10689, -60261, 116535, -304555, 268707, 7942071, -19570935, 9537731, 1117836325, -630737297, -52310180977, 618435378229, 523526983623, -3672122551119, 8661572895987, 1205887924659627, -8604836834766111, -77855893119175779
Offset: 0
-
T[n_, m_] := T[n, m] = If[n == m, 1, Binomial[m, n-m] - Sum[T[n, i]*T[i, m]/2, {i, m+1, n-1}]/2]; a[n_] := T[n, 1] // Numerator; Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Oct 29 2015, after Vladimir Kruchinin *)
-
T(n,m):= if n=m then 1 else (binomial(m,n-m) -sum(T(n,i) *T(i,m), i,m+1,n-1))/2; makelist(num(T(n,1)), n,1,7); /* Vladimir Kruchinin, Nov 08 2011 */
-
{a(n)=local(A,B,F=x+x^2+x*O(x^n));A=F; if(n==0,0, for(i=0,n, B=serreverse(A); A=(A+subst(B,x,F))/2); numerator(polcoeff(A,n,x)))}
Showing 1-2 of 2 results.
Comments