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Search: id:A116071
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| A116071 |
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Triangle T, read by rows, equal to Pascal's triangle to the matrix power of Pascal's triangle, so that T = C^C, where C(n,k) = binomial(n,k) and T(n,k) = A000248(n-k)*C(n,k). |
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+0
2
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| 1, 1, 1, 3, 2, 1, 10, 9, 3, 1, 41, 40, 18, 4, 1, 196, 205, 100, 30, 5, 1, 1057, 1176, 615, 200, 45, 6, 1, 6322, 7399, 4116, 1435, 350, 63, 7, 1, 41393, 50576, 29596, 10976, 2870, 560, 84, 8, 1, 293608, 372537, 227592, 88788, 24696, 5166, 840, 108, 9, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 = A000248 (Number of forests with n nodes and height at most 1). Column 1 = A052512 (Number of labeled trees of height 2). Row sums = A080108 (Sum_{k=1..n} k^(n-k)*C(n-1,k-1)). Central terms = A116072(n) = (n+1)*A000108(n)*A000248(n).
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FORMULA
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E.g.f. wrt x: A(x,y) = exp(x*exp(x)+x*y).
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EXAMPLE
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Triangle begins:
1;
1,1;
3,2,1;
10,9,3,1;
41,40,18,4,1;
196,205,100,30,5,1;
1057,1176,615,200,45,6,1;
6322,7399,4116,1435,350,63,7,1;
41393,50576,29596,10976,2870,560,84,8,1;
293608,372537,227592,88788,24696,5166,840,108,9,1; ...
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); n!*polcoeff(polcoeff(exp(X*exp(X)+X*Y), n, x), k, y)}
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CROSSREFS
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Cf. A000248, A052512, A080108, A116072.
Sequence in context: A100100 A102472 A101894 this_sequence A077756 A115080 A104219
Adjacent sequences: A116068 A116069 A116070 this_sequence A116072 A116073 A116074
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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), Feb 03 2006
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