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A169603
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Table T(n,k) = k*(4*n+2+k) read by rows.
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2
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0, 0, 7, 0, 11, 24, 0, 15, 32, 51, 0, 19, 40, 63, 88, 0, 23, 48, 75, 104, 135, 0, 27, 56, 87, 120, 155, 192, 0, 31, 64, 99, 136, 175, 216, 259, 0, 35, 72, 111, 152, 195, 240, 287, 336, 0, 39, 80, 123, 168, 215, 264, 315, 368, 423, 0, 43, 88, 135, 184, 235, 288, 343, 400
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OFFSET
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0,3
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COMMENTS
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These are the numerators of 1/(2n+1)^2-1/(2n+1+k)^2 as they appear in the energies of the hydrogen spectrum, not reduced by common factors with the denominators.
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REFERENCES
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Charles Janet, Considerations sur la structure du noyeau de l'atome, Decembre 1929, N 5, BEAUVAIS, page 39.
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LINKS
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Table of n, a(n) for n=0..63.
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EXAMPLE
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The table starts in row n=0 with columns 0<=k<=n as:
0; # A005563
0,7; # A061039
0,11,24; # A061043
0,15,32,51; # A061047
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CROSSREFS
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Row sums give: A169607 = 7*A000330, 7 times the sum of squares.
Sequence in context: A096408 A005481 A122699 * A097604 A007393 A225949
Adjacent sequences: A169600 A169601 A169602 * A169604 A169605 A169606
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KEYWORD
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nonn,frac,tabl
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AUTHOR
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Paul Curtz, Dec 03 2009
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STATUS
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approved
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