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A055894 Inverse Moebius transform of Pascal's triangle A007318. 2
1, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 4, 8, 4, 3, 2, 5, 10, 10, 5, 2, 4, 6, 18, 22, 18, 6, 4, 2, 7, 21, 35, 35, 21, 7, 2, 4, 8, 32, 56, 78, 56, 32, 8, 4, 3, 9, 36, 87, 126, 126, 87, 36, 9, 3, 4, 10, 50, 120, 220, 254, 220, 120, 50, 10, 4, 2, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for the first 101 rows, flattened

N. J. A. Sloane, Transforms

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

Triangle starts:

  [0]  1;

  [1]  1,   1;

  [2]  2,   2,   2;

  [3]  2,   3,   3,   2;

  [4]  3,   4,   8,   4,   3;

  [5]  2,   5,  10,  10,   5,   2;

  [6]  4,   6,  18,  22,  18,   6,   4;

  [7]  2,   7,  21,  35,  35,  21,   7,   2;

  [8]  4,   8,  32,  56,  78,  56,  32,   8,   4;

  [9]  3,   9,  36,  87, 126, 126,  87,  36,   9,   3;

  ...

MATHEMATICA

T[n_, k_] := DivisorSum[GCD[k, n], Binomial[n/#, k/#] &]; T[0, 0] = 1; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Dec 02 2015 *)

PROG

(PARI)

T(n, k) = if(n<=0, n==0, sumdiv(gcd(n, k), d, binomial(n/d, k/d) ) );

/* print triangle: */

{ for (n=0, 17, for (k=0, n, print1(T(n, k), ", "); ); print(); ); }

/* Joerg Arndt, Oct 21 2012 */

CROSSREFS

Row sums give A055895.

Sequence in context: A103183 A143901 A115263 * A224713 A168557 A194320

Adjacent sequences:  A055891 A055892 A055893 * A055895 A055896 A055897

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, Jun 09 2000

STATUS

approved

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Last modified February 22 16:10 EST 2019. Contains 320399 sequences. (Running on oeis4.)