Original entry on oeis.org
2, 15, 154, 1995, 31191, 571221, 11992688, 283976517, 7487521975, 217567092743, 6907888374828, 237951469523807, 8838510559556783, 352160268261051113, 14982705940607112640, 677935029521206050505, 32508195354031791206799
Offset: 1
Original entry on oeis.org
6, 120, 2340, 49315, 1142932, 29141994, 814059798, 24779916843, 817506518829, 29081010732059, 1110248649302494, 45298134089851175, 1967550159430960784, 90668183653348456484, 4418855084158930131012, 227122154996245283660487
Offset: 1
Original entry on oeis.org
2, 15, 120, 1190, 14595, 215950, 3761310, 75550188, 1721103648, 43872089118, 1237592664451, 38282002057156, 1288537309627464, 46886217384094764, 1834003542264708444, 76744318019878844916, 3420833746251201921980
Offset: 1
-
{a(n)=local(A=x, G=x*(1+x*y)/(1-x)); for(i=1, n+1, A=subst(G, x, A+O(x^(n+2))));polcoeff(polcoeff(A, n+1,x),n-1,y)}
Original entry on oeis.org
9, 154, 2340, 38325, 704102, 14570976, 337738758, 8697532008, 246819113442, 7660379273261, 258275171344333, 9403520522325228, 367786323703199388, 15381080863799688012, 684987041358431417024, 32366520461834117146792
Offset: 1
-
{a(n)=local(A=x, G=x*(1+x*y)/(1-x)); for(i=1, n+2, A=subst(G, x, A+O(x^(n+3))));polcoeff(polcoeff(A, n+2,x),n-1,y)}
A112317
Coefficients of x^n in the n-th iteration of (x + x^2) for n>=1.
Original entry on oeis.org
1, 2, 6, 30, 220, 2170, 27076, 409836, 7303164, 149837028, 3479498880, 90230486346, 2584679465160, 81056989408928, 2762187020749144, 101633218030586364, 4015771398425994048, 169588657820702174728
Offset: 1
The initial iterations of x + x^2 begin:
F(x) = (1)*x + x^2;
F(F(x)) = x + (2)*x^2 + 2*x^3 + x^4;
F(F(F(x))) = x + 3*x^2 + (6)*x^3 + 9*x^4+ 10*x^5+ 8*x^6+ 4*x^7+ x^8;
F(F(F(F(x)))) = x + 4*x^2 + 12*x^3 + (30)*x^4 + 64*x^5 +...;
F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + 70*x^4 + (220)*x^5 +...;
F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + 560*x^5 + (2170)*x^6 +...;
where the terms in parenthesis illustrate how to form this sequence.
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{a(n)=local(F=x+x^2, G=x+x*O(x^n));if(n<1,0, for(i=1,n,G=subst(F,x,G));return(polcoeff(G,n,x)))}
for(n=1, 30, print1(a(n), ", "))
Added cross-references and comments; name and example changed by
Paul D. Hanna, Feb 04 2011
Showing 1-5 of 5 results.
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