A371841 G.f. A(x) satisfies A(A(A(A(A(A(x)))))) = x + 6*x^2 + 36*x^3.
0, 1, 1, 1, -35, 325, -1295, -12455, 283285, -2186675, -5612255, 324564625, -2869315163, -12271744331, 490525545169, -2159646628535, -58485623789483, 634417586418781, 8780962428445537, -156001827155519807, -2145519156372933275, 50455156500263955781
Offset: 0
Keywords
Examples
A(A(x)) = x + 2*x^2 + 4*x^3 - 64*x^4 + 448*x^5 - 832*x^6 - 24704*x^7 + ... A(A(A(x))) = x + 3*x^2 + 9*x^3 - 81*x^4 + 405*x^5 + 243*x^6 - 28431*x^7 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..200
Formula
A372537 G.f. A(x) satisfies A(A(A(A(x)))) = x + 4*x^2 + 16*x^3.
0, 1, 1, 1, -15, 81, -159, -1695, 19857, -77775, -372351, 6628545, -24096975, -232640751, 2756221601, 2199811873, -210934282287, 553408050417, 17722961332929, -95716389015423, -1950283855292559, 15527782649242065, 285278599792984545, -3006768595808218911
Offset: 0
Keywords
Examples
A(A(x)) = x + 2*x^2 + 4*x^3 - 24*x^4 + 80*x^5 + 32*x^6 - 2496*x^7 + 14976*x^8 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..486
Formula
Define the sequence b(n,m) as follows. If n
Let B(x) = A(A(x)).
B(B(x)) = x + 4*x^2 + 16*x^3.
B(x) = F(2*x)/2, where F(x) is the g.f. for A220110.
A372521 G.f. A(x) satisfies A(A(A(A(A(x))))) = x + 5*x^2 + 25*x^3.
0, 1, 1, 1, -24, 176, -524, -5124, 87126, -506774, -1759824, 57671226, -358791624, -2206347624, 49453238976, -92944954824, -4824317301399, 31062072140001, 557647434392001, -6058153265478399, -93734220877891074, 1402372000511972226, 21436083233577492876
Offset: 0
Keywords
Formula
Define the sequence b(n,m) as follows. If n