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Search: id:A108556
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| A108556 |
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Triangle, read by rows, where row n equals the inverse binomial transform of the crystal ball sequence for D_n lattice. |
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+0
3
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| 1, 1, 2, 1, 4, 4, 1, 12, 30, 20, 1, 24, 120, 192, 96, 1, 40, 330, 940, 1080, 432, 1, 60, 732, 3200, 6240, 5568, 1856, 1, 84, 1414, 8708, 25200, 37184, 27104, 7744, 1, 112, 2480, 20352, 80960, 173824, 206080, 126976, 31744, 1, 144, 4050, 42588, 221544, 643824
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row n equals the inverse binomial transform of row n of the square array A108553.
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FORMULA
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Main diagonal equals A008353: 2^(n-1)*(2^n-n) for n>1.
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EXAMPLE
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Triangle begins:
1;
1,2;
1,4,4;
1,12,30,20;
1,24,120,192,96;
1,40,330,940,1080,432;
1,60,732,3200,6240,5568,1856;
1,84,1414,8708,25200,37184,27104,7744;
1,112,2480,20352,80960,173824,206080,126976,31744; ...
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PROGRAM
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(PARI) {T(n, k)=local(A=vector(n+1, r, vector(n+1, c, if(r-1==0|c-1==0, 1, if(r-1==1, 2*c-1, sum(j=0, c-1, binomial(r+c-j-2, c-j-1)*(binomial(2*r-2, 2*j)-2*(r-1)*binomial(r-3, j-1)))))))); polcoeff(subst(Ser(A[n+1]), x, x/(1+x))/(1+x), k)}
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CROSSREFS
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Cf. A108553, A108557 (row sums), A108558, Rows are inverse binomial transforms of: A001844 (row 2), A005902 (row 3), A007204 (row 4), A008356 (row 5), A008358 (row 6), A008360 (row 7), A008362 (row 8), A008377 (row 9), A008379 (row 10).
Adjacent sequences: A108553 A108554 A108555 this_sequence A108557 A108558 A108559
Sequence in context: A134308 A117427 A097761 this_sequence A122440 A046943 A107728
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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 10 2005
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