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
A372500 G.f. A(x) satisfies A(A(A(x))) = Sum_{k>=1} k^2 * 9^(k-1) * x^k.
0, 1, 12, -45, 1404, -33048, 684288, -5847309, -440129376, 30809872071, -952939532952, -1846906652457, 1545045542366472, -30949156972076031, -4367665752590389608, 253458876292612253442, 14695464346775699515704, -2012792131604632851142020
Offset: 0
Keywords
Examples
A(A(x)) = x + 24*x^2 + 198*x^3 + 1836*x^4 + 8667*x^5 - 139968*x^6 + 11814903*x^7 - 371755008*x^8 + ...
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