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Search: id:A102321
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| A102321 |
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Column 0 of triangular matrix A102320, which satisfies T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1). |
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+0
3
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| 1, 1, 4, 33, 436, 8122, 197920, 6007205, 219413116, 9402081718, 463548752912, 25893783163498, 1618536618626888, 112053082721454708, 8518619080226661504, 705977323976245345133, 63382036275445226941548
(list; table; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: 1 = Sum_{n>=0} a(n)*x^n*prod_{k=0, n} (1-(2k+1)*x) for n>0 with a(0)=1.
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EXAMPLE
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G.f.: 1 = (1-x) + 1*x*(1-x)(1-3x) + 4*x^2*(1-x)(1-3x)(1-5x) + ... + a(n)*x^n*(1-x)(1-3x)(1-5x)*..*(1-(2n+1)*x) + ...
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PROGRAM
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(PARI) {a(n)=local(A=Mat(1), B); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=2*j-1, if(j==1, B[i, j]=(A^2)[i-1, 1], B[i, j]=(A^2)[i-1, j])); )); A=B); return(A[n+1, 1])}
(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k*prod(j=0, k, 1-(2*j+1)*x+x*O(x^n))), n))}
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CROSSREFS
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Cf. A102087, A102323.
Sequence in context: A111534 A052885 A119821 this_sequence A002190 A101981 A002018
Adjacent sequences: A102318 A102319 A102320 this_sequence A102322 A102323 A102324
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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), Jan 05 2005
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