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A025015
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Central decanomial coefficients: largest coefficient of (1+x+...+x^9)^n.
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3
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1, 1, 10, 75, 670, 6000, 55252, 512365, 4816030, 45433800, 432457640, 4123838279, 39581170420, 380242296850, 3671331273480, 35460394945125, 343900019857310, 3335361909606710, 32458256583753952, 315825118347405835
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of integers in [0, 10^n-1] whose sums of digits are equal to the most common value, which is 9*n/2 for even n and (9*n +/- 1)/2 for odd n > 1. E.g. The most common value of sums of digits of numbers from 0 to 9999 is 9*4/2 = 18, so there are a(4)=670 numbers in this range whose sums of digits are 18. - Warut Roonguthai (warut822(AT)yahoo.com), Jun 08 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
| a(n) = sum((-1)^(k)*binomial(n, k)*binomial(n+floor(9*n/2)-10*k-1, n-1), k=0..floor(9*n/20)). - Warut Roonguthai (warut822(AT)yahoo.com), Jun 08 2006
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CROSSREFS
| Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025013, A025014
Sequence in context: A026935 A110127 A081017 * A049392 A136869 A108277
Adjacent sequences: A025012 A025013 A025014 * A025016 A025017 A025018
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KEYWORD
| easy,nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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