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Search: id:A101343
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| A101343 |
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Triangle read by rows: nonzero coefficients of the polynomials F_n(x) which express derivatives of tan z in terms of powers of tan z. |
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+0
1
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| 1, 1, 1, 2, 2, 6, 8, 2, 24, 40, 16, 120, 240, 136, 16, 720, 1680, 1232, 272, 5040, 13440, 12096, 3968, 272, 40320, 120960, 129024, 56320, 7936, 362880, 1209600, 1491840, 814080, 176896, 7936, 3628800, 13305600, 18627840, 12207360, 3610112, 353792
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OFFSET
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0,4
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COMMENT
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Interpolates between factorials and tangent numbers.
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 2nd ed. 1998, p. 287.
Knuth, D. E. and Buckholtz, Thomas J., Computation of tangent, Euler, and Bernoulli numbers. Math. Comp. 21 1967 663-688.
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EXAMPLE
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For example, D tan z = (tan z)^2 + 1.
Array begins:
1
1 1
2 2
6 8 2
24 40 16
120 240 136 16
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CROSSREFS
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Reflection of triangle A008293.
Sequence in context: A099577 A106168 A106166 this_sequence A134457 A092522 A116542
Adjacent sequences: A101340 A101341 A101342 this_sequence A101344 A101345 A101346
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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D. E. Knuth, Jan 28 2005
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu) and R. Stephan, Jan 30 2005
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