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A034140
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Number of partitions of n into distinct parts from [ 1,2,3,...,10 ].
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0
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1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 27, 29, 31, 33, 35, 36, 38, 39, 39, 40, 40, 39, 39, 38, 36, 35, 33, 31, 29, 27, 24, 22, 20, 17, 15, 13, 11, 10, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| The number of different ways to run up a staircase with 10 steps, taking steps of odd sizes (or taking steps of distinct sizes), where the order is not relevant and there is no other restriction on the number or the size of each step taken is the coefficient of x^10.
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REFERENCES
| Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem II, Missouri Journal of Mathematical Sciences, Vol. 16, No. 1, Winter 2004, pp. 12-17. Zentralblatt MATH, Zbl 1071.05501.
Mohammad K. Azarian, A Generalization of the Climbing Stairs Problem, Mathematics and Computer Education, Vol. 31, No. 1, pp. 24-28, Winter 1997. MathEduc Database (Zentralblatt MATH, 1997c.01891).
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FORMULA
| Expansion of (1+x)*(1+x^2)*(1+x^3)*...*(1+x^10).
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MATHEMATICA
| Join[CoefficientList[Series[Times@@Table[1+x^n, {n, 10}], {x, 0, 64}], x], Table[0, {8}]] (* From Harvey P. Dale, June 17 2011 *)
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CROSSREFS
| Sequence in context: A185225 A027196 A100928 * A109950 A008674 A067596
Adjacent sequences: A034137 A034138 A034139 * A034141 A034142 A034143
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Added a comment and 2 references by Mohammad K. Azarian (azarian(AT)evansville.edu), Aug 22 2010
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