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A124380
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O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + k*x).
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2
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1, 1, 2, 4, 9, 22, 57, 157, 453, 1368, 4296, 13995, 47138, 163779, 585741, 2152349, 8113188, 31326760, 123748871, 499539900, 2058542819, 8651755865, 37054078481, 161591063250, 717032333816, 3235298221401, 14834735654080, 69085973044125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The Kn11 triangle sums of A094638 are given by the terms of this sequence. For the definitions of this and other triangle sums see A180662. [From Johannes W. Meijer, Apr 20 2011]
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FORMULA
| O.g.f.: A(x) = 1 + x*(1+x)/(G(0) - x*(1+x)) ; G(k) = 1+x*(k*x+x+1) - x*(k*x + 2*x + 1)/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 02 2011
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EXAMPLE
| A(x) = 1 + x*(1+x) + x^2*(1+x)*(1+2x) + x^3*(1+x)*(1+2x)*(1+3x) +...
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PROG
| (PARI) a(n)=polcoeff(sum(k=0, n, x^k*prod(j=0, k, 1+j*x+x*O(x^n))), n)
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CROSSREFS
| Sequence in context: A105633 A196161 A099241 * A176084 A192576 A059019
Adjacent sequences: A124377 A124378 A124379 * A124381 A124382 A124383
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006
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