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Search: id:A096542
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| A096542 |
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Triangle, read by rows, where e.g.f. A(x,y) satisfies: A(x,y) = exp(x*y*A(x,y+1)) and A(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k)/n!*x^n*y^k. |
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+0
4
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| 1, 0, 1, 0, 2, 3, 0, 15, 30, 16, 0, 244, 564, 444, 125, 0, 6885, 17540, 16680, 7320, 1296, 0, 298326, 817470, 877740, 478380, 136590, 16807, 0, 18377191, 53352138, 62582100, 39142600, 14146440, 2873136, 262144, 0, 1525885992, 4645224472
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums form A096537. Main diagonal forms A000272 (labeled trees on n nodes). Secondary diagonal forms 2*A057500 (labeled connected graphs with n edges and n nodes). Other diagonals include 3*A096543 and 4*A096544.
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FORMULA
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E.g.f. satisfies: A(x, y+1) = log(A(x, y))/(x*y). T(n, 1) = n*A096537(n). T(n, n) = n^(n-2) = A000272(n). T(n, n-1) = 2*A057500(n).
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EXAMPLE
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A(x,y) = exp(x*y*exp(x*(y+1)*exp(x*(y+2)*exp(...exp(x*(n+y)*exp(...))...)))).
Rows begin:
[1],
[0,1],
[0,2,3],
[0,15,30,16],
[0,244,564,444,125],
[0,6885,17540,16680,7320,1296],
[0,298326,817470,877740,478380,136590,16807],
[0,18377191,53352138,62582100,39142600,14146440,2873136,262144],...
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PROGRAM
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(PARI) {T(n, k)=local(A=exp(x)); for(i=1, n, A=exp(x*(n-i+y)*A+x*O(x^n)+y*O(y^k))); n!*polcoeff(polcoeff(A, k, y), n, x)}
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CROSSREFS
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Cf. A096537, A000272, A057500, A096543, A096544.
Sequence in context: A059740 A005160 A085042 this_sequence A009206 A088874 A002634
Adjacent sequences: A096539 A096540 A096541 this_sequence A096543 A096544 A096545
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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 25 2004
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