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Search: id:A134093
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| 1, 4, 30, 215, 1729, 15176, 143814, 1462995, 15876410, 182811992, 2223580281, 28458251185, 381943459065, 5359649816728, 78430018675440, 1194057733357517, 18873870914263424, 309154787519651284, 5238840625331179517
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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+3} C(n+3,k)*x^k/(1-k*x)^3 / [Product_{i=1..k}(1-i*x)].
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PROGRAM
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(PARI) {a(n)= polcoeff(sum(k=0, n+3, binomial(n+3, k)*x^k/(1-k*x)^3/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, A134092; A134094 (row sums); A048993 (S2).
Sequence in context: A089154 A113450 A094567 this_sequence A007905 A084976 A000313
Adjacent sequences: A134090 A134091 A134092 this_sequence A134094 A134095 A134096
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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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