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Search: id:A130513
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| A130513 |
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Subtriangle of triangle in A051168 : remove central column of A051168 and all columns to the right; now read by upwards diagonals. |
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+0
1
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| 1, 1, 0, 2, 1, 0, 5, 2, 1, 0, 14, 7, 3, 1, 0, 42, 20, 9, 3, 1, 0, 132, 66, 30, 12, 4, 1, 0, 429, 212, 99, 40, 15, 4, 1, 0, 1430, 715, 333, 143, 55, 18, 5, 1, 0, 4862, 2424, 1144, 497, 200, 70, 22, 5, 1, 0, 16796, 8398, 3978, 1768, 728, 273, 91, 26, 6, 1, 0, 58786, 29372, 13995
(list; table; graph; listen)
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OFFSET
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1,4
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REFERENCES
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A. Errera, Analysis situs: un probleme d'enumeration, Memoires Acad. Bruxelles (1931), Serie 2, Vol. 11, No. 6, 26pp.
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FORMULA
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Sum_{k, 1<=k<=n} T(n,k) = A022553(n); Sum_{k, 1<=k<=n}k*T(n,k) = A002996(n) .
1/(2n-k) Sum( d | gcd(2n-k,n-k) ; mu(d) C((2n-k)/d,(n-k)/d) ) - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jul 20 2008
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EXAMPLE
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Triangle T(n,k), 1<=k<=n, begins:
1;
1, 0;
2, 1, 0;
5, 2, 1, 0;
14, 7, 3, 1, 0;
42, 20, 9, 3, 1, 0;
132, 66, 30, 12, 4, 1, 0;
429, 212, 99, 40, 15, 4, 1, 0;
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MATHEMATICA
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Table[1/(2n-k) Plus@@ (MoebiusMu[ # ]Binomial[(2n-k)/#, (n-k)/# ]&/@ Divisors[GCD[2n-k, n-k]]), {n, 12}, {k, n}] - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jul 20 2008
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CROSSREFS
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Cf. A000108 A000150 A050181 A050182 A050183 A050184 A050185.
Sequence in context: A143445 A133727 A103185 this_sequence A114596 A083417 A021479
Adjacent sequences: A130510 A130511 A130512 this_sequence A130514 A130515 A130516
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 08 2007
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 08 2007
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