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triangle, row sums = primes

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  • purushaz
    00 %S A124800 2,2,1,2,2,1,2,3,3,1,2,4,6,4,3,2,5,10,10,15,9,2,6,15,20,45,54,23,2,7,21, %T A124800 35,105,189,161,53,2,8,28,56,210,504,644,424,115 %V A124800
    Message 1 of 1 , Nov 9, 2006
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      00
      %S A124800
      2,2,1,2,2,1,2,3,3,1,2,4,6,4,3,2,5,10,10,15,9,2,6,15,20,45,54,23,2,7,21,
      %T A124800 35,105,189,161,53,2,8,28,56,210,504,644,424,115
      %V A124800
      2,2,1,2,2,1,2,3,3,-1,2,4,6,-4,3,2,5,10,-10,15,-9,2,6,15,-20,45,-54,23,2,7,21,-35,105,
      %W A124800 -189,161,-53,2,8,28,-56,210,-504,644,-424,115
      %N A124800 Triangle, row sums = primes.
      %C A124800 Right border = A007442, (2, 1, 1, -1, 3, -9...) inverse
      binomial transform of the primes.
      %F A124800 Let M = a diagonalized infinite matrix of A007442, inverse
      binomial transform of the primes, and P = Pascal's triangle as an
      infinite lower triangular matrix. Then the triangle A124800 = P*M,
      deleting the zeros.
      %e A124800 First few rows of the triangle are:
      %e A124800 2;
      %e A124800 2, 1;
      %e A124800 2, 2, 1;
      %e A124800 2, 3, 3, -1;
      %e A124800 2, 4, 6, -4, 3;
      %e A124800 2, 5, 10, 10, 15, -9;
      %e A124800 2, 6, 15, -20, 45, -54, 23;
      %e A124800 2, 7, 21, -35, 105, -189, 161, -53;
      %e A124800 ..
      %e A124800 Row 5 sum = 11 = p5 since (2 + 4 + 6 - 4 + 3) = 11.
      %Y A124800 Cf. A007442.
      %K A124800 nonn,tabl,new
      %O A124800 1,1
      %A A124800 Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 07 2006
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