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A134092
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Column 2 of triangle A134090.
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4
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1, 3, 18, 110, 780, 6167, 53494, 504030, 5112090, 55411697, 638154165, 7770348170, 99618149267, 1339889000543, 18848892749144, 276573551651632, 4222814264496510, 66947348027905977, 1099955438013660173
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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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PROG
| (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
| Cf. A134090; columns: A122455, A134091, A134093; A134094 (row sums); A048993 (S2).
Sequence in context: A037655 A074571 A114311 * A000274 A193236 A199259
Adjacent sequences: A134089 A134090 A134091 * A134093 A134094 A134095
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 08 2007
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