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A130513 Subtriangle of triangle in A051168: remove central column of A051168 and all columns to the right; now read by upwards diagonals. 0
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; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

A. Errera, Analysis situs: Un problème d'énumération, Memoires Acad. Bruxelles (1931), Serie 2, Vol. 11, No. 6, 26pp.

LINKS

Table of n, a(n) for n=1..69.

FORMULA

Sum_{k, 1<=k<=n} T(n,k) = A022553(n); Sum_{k, 1<=k<=n}k*T(n,k) = A002996(n).

T(n,k) = 1/(2n-k) Sum( d | gcd(2n-k,n-k) = mu(d) C((2n-k)/d,(n-k)/d) ). - Wouter Meeussen, Jul 20 2008

EXAMPLE

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;

MATHEMATICA

Table[1/(2n-k) Plus@@ (MoebiusMu[ # ]Binomial[(2n-k)/#, (n-k)/# ]&/@ Divisors[GCD[2n-k, n-k]]), {n, 12}, {k, n}] (* Wouter Meeussen, Jul 20 2008 *)

CROSSREFS

Cf. A000108, A000150, A050181, A050182, A050183, A050184, A050185.

Sequence in context: A143445 A133727 A103185 * A114596 A083417 A021479

Adjacent sequences:  A130510 A130511 A130512 * A130514 A130515 A130516

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Aug 08 2007

EXTENSIONS

Edited by N. J. A. Sloane, Oct 08 2007

STATUS

approved

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Last modified January 26 19:45 EST 2021. Contains 340442 sequences. (Running on oeis4.)