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Search: id:A134094
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| 1, 2, 6, 26, 140, 887, 6405, 51564, 455712, 4370567, 45081476, 496556194, 5806502663, 71734434956, 932447207866, 12707973761320, 181033752071568, 2688530124711819, 41525910256013832, 665674913113633582
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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} C(n,k)*x^k*(1-k*x) / [Product_{i=0..k+1}(1-i*x)], equivalently, a(n) = Sum_{k=0..n} C(n,k)*[S2(n,k) - k*S2(n-1,k)], where S2(n,k) = A048993(n,k) are Stirling numbers of the 2nd kind.
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*polcoeff((1-k*x)/prod(i=0, k+1, 1-i*x+x*O(x^(n))), n-k))}
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CROSSREFS
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Cf. A134090; columns: A122455, A134091, A134092, A134093; A048993 (S2).
Adjacent sequences: A134091 A134092 A134093 this_sequence A134095 A134096 A134097
Sequence in context: A030957 A030898 A002788 this_sequence A009575 A127116 A107404
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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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