A372499 G.f. satisfies A(A(A(x))) = F(x), where F(x) is the g.f. for A053540(n) = n*9^(n-1).
0, 1, 6, 9, 54, 0, -1944, 44469, -323676, -5990193, 179194032, 484654509, -105337511100, 757846026261, 85419734244300, -1707846638480514, -90276038133498612, 3464956887464464164, 118426852966952180502, -7984363576091338944720, -181143285020960488524558
Offset: 0
Keywords
Examples
A(A(x)) = x + 12*x^2 + 90*x^3 + 594*x^4 + 3807*x^5 + 20412*x^6 + 123201*x^7 + 1032264*x^8 - 1463103*x^9 - 35468766*x^10 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..200
Formula
Define the sequence b(n,m) as follows. If n
A372522 G.f. A(x) satisfies A(A(A(A(A(A(x)))))) = Sum_{k>=1} k * 18^(k-1) * x^k.
0, 1, 6, -18, 378, -5670, 52488, 930204, -55108026, 575622774, 46483766460, -1494416264796, -85327731650772, 5947844644410876, 192190798316367540, -29067440301002581416, -418574641900663175706, 179341053539746099078422
Offset: 0
Keywords
Examples
A(A(x)) = x + 12*x^2 + 36*x^3 + 432*x^4 - 62208*x^6 + 2846016*x^7 - ... A(A(A(x))) = x + 18*x^2 + 162*x^3 + 1458*x^4 + 13122*x^5 + 2125764*x^7 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..200
Formula
A372520 G.f. A(x) satisfies A(A(A(A(A(x))))) = Sum_{k>=1} k * 25^(k-1) * x^k.
0, 1, 10, -25, 1000, -18125, 131250, 11609375, -630156250, 4314062500, 1173535156250, -38006699218750, -4262573730468750, 321379049072265625, 20787043081054687500, -3209395283374023437500, -116229452332824707031250, 39638105812041778564453125
Offset: 0
Keywords
Formula
Define the sequence b(n,m) as follows. If n