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Search: id:A118588
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| A118588 |
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Triangle generated by e.g.f.: A(x,y) = exp(x + y*(x^2+x^3)), read by rows of length [n/2+1]. |
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+0
3
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| 1, 1, 1, 2, 1, 12, 1, 36, 12, 1, 80, 180, 1, 150, 1260, 120, 1, 252, 5460, 3360, 1, 392, 17640, 43680, 1680, 1, 576, 46872, 342720, 75600, 1, 810, 108360, 1839600, 1587600, 30240, 1, 1100, 225720, 7539840, 20235600, 1995840, 1, 1452, 433620, 25391520
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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E.g.f. V(x) of eigenvector A119013 satisfies: V(x) = exp(x)*V(x^2+x^3); note the similarity to e.g.f. of this triangle.
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EXAMPLE
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Triangle begins:
1;
1;
1,2;
1,12;
1,36,12;
1,80,180;
1,150,1260,120;
1,252,5460,3360;
1,392,17640,43680,1680;
1,576,46872,342720,75600; ...
O.g.f. for columns:
0!/0!*(1)/(1-x);
2!/1!*(1+2*x)/(1-x)^4;
4!/2!*(1+8*x+21*x^2)/(1-x)^7;
6!/3!*(1+18*x+129*x^2+356*x^3)/(1-x)^10;
8!/4!*(1+32*x+438*x^2+2984*x^3+8425*x^4)/(1-x)^13; ...
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PROGRAM
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(PARI) {T(n, k)=n!*polcoeff(polcoeff(exp(x+y*(x^2+x^3)+x*O(x^n)+y*O(y^k)), n, x), k, y)}
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CROSSREFS
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Cf. A118589 (row sums), A119013 (eigenvector).
Sequence in context: A105608 A051190 A072512 this_sequence A058734 A103187 A107722
Adjacent sequences: A118585 A118586 A118587 this_sequence A118589 A118590 A118591
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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), May 08 2006
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