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Search: id:A121372
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| A121372 |
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Triangle, read by rows of length A003056(n) for n>=1, defined by the recurrence: T(n,k) = T(n-k,k-1) - T(n-k,k) for n>k>1, with T(n,1)=(-1)^(n-1) for n>=1. |
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+0
1
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| 1, -1, 1, 1, -1, -1, 1, 0, -1, 0, 1, 1, 1, -1, -1, -1, 0, 1, 0, -1, -1, 0, 2, 1, 1, 1, -1, -1, -1, -1, 1, 0, 1, 0, -2, -1, -1, 0, 2, 1, 1, 1, -2, 0, 1, -1, -1, 2, 1, -1, 1, 0, -2, -1, 0, -1, 0, 3, 1, -1, 1, 1, -3, -2, 1, -1, -1, 2, 1, -1, 1, 0, -3, -1, 2, 1, -1, 0, 4, 2, -1, -1, 1, 1, -3, -1, 2, 0, -1, -1, 3, 1, -3, -1, 1, 0, -4, -2, 2, 1, -1, 0, 4, 2, -3
(list; table; graph; listen)
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OFFSET
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1,23
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COMMENT
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Row sums equal A003406 (offset 1), the expansion of Ramanujan's function: R(x) = 1 + Sum_{n>=1} { x^(n*(n+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^n)) }.
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FORMULA
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G.f. of column k: x^(k*(k+1)/2) / ((1+x)(1+x^2)(1+x^3)...(1+x^k)) for k>=1.
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EXAMPLE
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Triangle begins:
1;
-1;
1, 1;
-1,-1;
1, 0;
-1, 0, 1;
1, 1,-1;
-1,-1, 0;
1, 0,-1;
-1, 0, 2, 1;
1, 1,-1,-1;
-1,-1, 1, 0;
1, 0,-2,-1;
-1, 0, 2, 1;
1, 1,-2, 0, 1;
-1,-1, 2, 1,-1;
1, 0,-2,-1, 0;
-1, 0, 3, 1,-1;
1, 1,-3,-2, 1;
-1,-1, 2, 1,-1;
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PROGRAM
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(PARI) {T(n, k)=if(n<k|k<1, 0, if(n==1, 1, T(n-k, k-1)-T(n-k, k)))}
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CROSSREFS
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Cf. A003406, A008289.
Sequence in context: A037912 A056980 A005094 this_sequence A123706 A025452 A054977
Adjacent sequences: A121369 A121370 A121371 this_sequence A121373 A121374 A121375
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2006
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