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Search: id:A084784
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| A084784 |
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Binomial transform = self-convolution: first column of the triangle (A084783). |
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+0
9
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| 1, 1, 2, 6, 25, 137, 944, 7884, 77514, 877002, 11218428, 160010244, 2516742498, 43260962754, 806650405800, 16213824084864, 349441656710217, 8037981040874313, 196539809431339642, 5090276002949080318
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In the triangle (A084783), the diagonal (A084785) is the self-convolution of this sequence, and the row sums (A084786) gives the differences of the diagonal and this sequence.
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FORMULA
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G.f. satisfies A(n*x)^2 = n-th binomial transform of A(n*x).
G.f. A(x) satisfies 1+x = A(x/(1+x))^2/A(x). - Michael Somos Feb 16 2006
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=1; for(k=1, n, A=truncate(A+O(x^k))+x*O(x^k); A+=A-1/subst(A^-2, x, x/(1+x))/(1+x); ); polcoeff(A, n))} /* Michael Somos Feb 18 2006 */
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CROSSREFS
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Cf. A084783, A084785, A084786.
Sequence in context: A102812 A020100 A128230 this_sequence A135881 A007815 A109286
Adjacent sequences: A084781 A084782 A084783 this_sequence A084785 A084786 A084787
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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 13 2003
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