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Search: id:A130522
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| A130522 |
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Diagonal immediately below the main diagonal of triangle A130521. |
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+0
2
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| 1, 1, 3, 8, 25, 89, 349, 1496, 6962, 34861, 186678, 1063591, 6418167, 40860485, 273513831, 1919284246, 14080876273, 107750778177, 858195666410, 7100543662976, 60922480229704, 541193416875432, 4970306167860426
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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G.f. of column 0 (A127782) satisfies: G(x) = 1 + x*G(x+x^2); main diagonal of triangle A130521 equals column 0 shift left one place.
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FORMULA
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a(n) = Sum_{k=0..[n/2]+1} [C(n-k,k) + C(n-k+1,k-1)]*a(n-k-1) for n>=2, with a(0)=a(1)=1.
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, if(n<=1, 1, sum(k=0, n\2+1, (binomial(n-k, k)+binomial(n-k+1, k-1))*a(n-k-1))))}
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CROSSREFS
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Cf. A130521 (triangle), A127782 (column 0).
Sequence in context: A148799 A148800 A033483 this_sequence A006219 A009268 A024430
Adjacent sequences: A130519 A130520 A130521 this_sequence A130523 A130524 A130525
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 02 2007
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