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Search: id:A134092
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| 1, 3, 18, 110, 780, 6167, 53494, 504030, 5112090, 55411697, 638154165, 7770348170, 99618149267, 1339889000543, 18848892749144, 276573551651632, 4222814264496510, 66947348027905977, 1099955438013660173
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OFFSET
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0,2
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COMMENT
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Row n of triangle T=A134090 = row n of (I + D*C)^n for n>=0 where C denotes Pascal's triangle, I the identity matrix, and D a matrix where D(n+1,n)=1 and zeros elsewhere.
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FORMULA
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a(n) = [x^n] Sum_{k=0..n+2} C(n+2,k)*x^k/(1-k*x)^2 / [Product_{i=1..k}(1-i*x)].
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PROGRAM
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(PARI) {a(n)= polcoeff(sum(k=0, n+2, binomial(n+2, k)*x^k/(1-k*x)^2/prod(i=0, k, 1-i*x +x*O(x^n))), n)}
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CROSSREFS
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Cf. A134090; columns: A122455, A134091, A134093; A134094 (row sums); A048993 (S2).
Adjacent sequences: A134089 A134090 A134091 this_sequence A134093 A134094 A134095
Sequence in context: A037655 A074571 A114311 this_sequence A000274 A054122 A074566
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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), Oct 08 2007
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