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Search: id:A089949
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| A089949 |
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Triangle T(n,k), read by rows, given by : [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where DELTA is the operator defined in A084938. |
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+0
10
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| 1, 0, 1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 12, 34, 24, 0, 1, 20, 110, 210, 120, 0, 1, 30, 270, 974, 1452, 720, 0, 1, 42, 560, 3248, 8946, 11256, 5040, 0, 1, 56, 1036, 8792, 38338, 87504, 97296, 40320, 0, 1, 72, 1764, 20580, 129834, 463050, 920184, 930960, 362880
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Diagonals : A000007 A000012 A002378; A000142 . Row sums : A003319
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FORMULA
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Sum_{k = 0...n} x^(n-k)*T(n, k) = A111528(x, n); see A000142, A003319, A111529, A111530, A111531, A111532, A111533 for x = 0, 1, 2, 3, 4, 5, 6 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 09 2005
Sum_{k, 0<=k<=n} T(n, k)*3^k = A107716(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 15 2005
Sum_{k, 0<=k<=n} T(n, k)*2^k = A000698(n+1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 15 2005
G.f.: A(x, y) = (1/x)*(1 - 1/(1 + Sum_{n>=1} [Prod_{k=0..n-1}(1+k*y)]*x^n )). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 16 2005
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EXAMPLE
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Triangle begins:
1;
0,1;
0,1,2;
0,1,6,6;
0,1,12,34,24;
0,1,20,110,210,120;
0,1,30,270,974,1452,720; ...
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PROGRAM
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(PARI) {T(n, k)=if(n<k|k<0, 0, if(n==0, 1, if(k==0, 0, polcoeff(polcoeff( (1-1/(1+sum(m=1, n+k, prod(j=0, m-1, 1+j*y)*x^m)))/x +x*O(x^n), n, x)+y*O(y^k), k, y))))} (Hanna)
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CROSSREFS
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Cf. A084938.
Sequence in context: A059299 A128722 A114709 this_sequence A085845 A138106 A131689
Adjacent sequences: A089946 A089947 A089948 this_sequence A089950 A089951 A089952
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 11 2004
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