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Search: id:A120568
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| A120568 |
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Triangle, read by rows, where the k-th column equals the k-th self-composition of column 1 (A120567) for k>=0, such that row sums equal column 1. |
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2
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| 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 6, 3, 1, 0, 15, 21, 12, 4, 1, 0, 53, 82, 54, 20, 5, 1, 0, 215, 351, 263, 110, 30, 6, 1, 0, 976, 1630, 1364, 644, 195, 42, 7, 1, 0, 4859, 8151, 7469, 3956, 1335, 315, 56, 8, 1, 0, 26150, 43627, 42971, 25304, 9505, 2470, 476, 72, 9, 1
(list; table; graph; listen)
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OFFSET
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0,8
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EXAMPLE
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The successive self-compositions of the g.f. of column 1 begin:
F(x) = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 53*x^6 + 215*x^7 + 976*x^8+...
F(F(x)) = x + 2*x^2 + 6*x^3 + 21*x^4 + 82*x^5 + 351*x^6 + 1630*x^7 +...
F(F(F(x))) = x + 3*x^2 + 12*x^3 + 54*x^4 + 263*x^5 + 1364*x^6 +...
F(F(F(F(x)))) = x + 4*x^2 + 20*x^3 + 110*x^4 + 644*x^5 + 3956*x^6 +...
F(F(F(F(F(x))))) = x + 5*x^2 + 30*x^3 + 195*x^4 + 1335*x^5 +9505*x^6+...
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 2, 2, 1;
0, 5, 6, 3, 1;
0, 15, 21, 12, 4, 1;
0, 53, 82, 54, 20, 5, 1;
0, 215, 351, 263, 110, 30, 6, 1;
0, 976, 1630, 1364, 644, 195, 42, 7, 1;
0, 4859, 8151, 7469, 3956, 1335, 315, 56, 8, 1;
0, 26150, 43627, 42971, 25304, 9505, 2470, 476, 72, 9, 1;
0, 150585, 248631, 258976, 167804, 69899, 20023, 4207, 684, 90, 10, 1;
where column k equals the k-th self-composition of column 1.
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CROSSREFS
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Cf. A120567 (column 1).
Adjacent sequences: A120565 A120566 A120567 this_sequence A120569 A120570 A120571
Sequence in context: A110281 A120059 A067347 this_sequence A065066 A064045 A110314
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 14 2006
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