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By N. J. A. Sloane

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Often these are called the Euler numbers instead of seq. ) The odd numbered Euler numbers form seq. 829: 1, 2, 16, 272, 7936, 353792,. , and are called the tangent numbers Tn = Ε*>η-λ. They have gf x -f- 2γ} + 16-r-j + · · · = tan x. E{=\ E,= 1 \ 12 E3 = 2 13 2 2 31 E4 = 5 1324 1423 £5=16 13254 15342 25143 35142 14253 23154 25341 35241 Fig. 25. 2314 14352 24153 34152 45132 2413 3412 15243 24351 34251 45231 Seq. 587, the Euler numbers. The Bernoulli numbers Bn are defined by D n = 2nE2n-1 22w(22w — 1) ' and form the sequence 1 1 1 1 5 691 7 3617 6 ' 3 0 ' 4 2 ' 3 0 ' 6 6 ' 2 7 3 0 ' 6 ' 510 " " " with gf x 2 1 x2 6 2!

250 1,2,3, 5, 7, 17,31, 89, 127, 521, 607, 1279, 2281, 3217, 4423, 9689 IRREDUCIBLE MERSENNE TRINOMIALS. REF IC 15 68 69. 251 1 , 2 , 3 , 5 , 8 , 9 , 10, 11, 12, 18, 19,22,26,28,30,31,33,35,36,38,39,40,41,44, 46, 47, 48, 50, 52, 54, 55, 56, 58, 61. 62, 66, 67, 68, 69, 71, 72, 74, 76, 77, 80, 82, 83, 91 ELLIPTIC CURVES. REF JRAM 212 23 63. 252 1, 2, 3, 5, 8, 11, 12, 14. 18, 20, 21, 27, 29, 30, 32, 35, 44, 45, 48, 50 OF THE FORM 2X**2 + 3Y**2. REF EUL (1) 1 425 11. 253 1, 2, 3, 5, 8. 12. 18, 26, 38, 53, 75, 103, 142, 192, 260, 346, 461, 605, 796 PLANAR PARTITIONS.

112 1 , 2 , 2 , 4 , 4 , 6 , 7 , 10, 11, 16, 17,23,26,33,37,47,52,64,72,86,96, 115, 127, 149, 166, 192, 212, 245, 269, 307, 338, 382, 419, 472, 515, 576, 629, 699, 760, 843, 913 EXPANSION OF A GENERATING FUNCTION. REF CAY 10 415. 113 1 , 2 , 2 , 4 , 4 , 7 , 8 , 1 2 , 14,21,24,34,41,55,66,88, 105, 137, 165,210,253,320, 383, 478, 574, 708, 847, 1039, 1238, 1507, 1794, 2167, 2573, 3094, 3660, 4378, 5170 PARTITIONS WITH NO PART OF SIZE 1. REF TA1 1 334. AS1 836. 114 1 , 2 , 2 , 4 , 4 , 8 , 9 , 18,23,44,63, 122, 190,362,612, 1162,2056,3912,7155, 13648 NECKLACES.

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