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Search: id:A151775
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| A151775 |
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Triangle read by rows: T(n,k) = value of (d^2n/dx^2n) (tan^{2k}(x)/cos(x)) at the point x = 0. |
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+0
1
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| 1, 1, 2, 5, 28, 24, 61, 662, 1320, 720, 1385, 24568, 83664, 100800, 40320, 50521, 1326122, 6749040, 13335840, 11491200, 3628800, 2702765, 98329108, 692699304, 1979524800, 2739623040, 1836172800, 479001600, 199360981, 9596075582
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009: (Start)
T(n,0)=A000364(n), the Euler (or secant) numbers.
Sum of entries in row n = A000281(n).
(End)
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REFERENCES
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C. Radoux, The Hankel determinant ..., Amer. Math. Monthly, 109 (2002), 277-278.
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EXAMPLE
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Triangle begins:
1
1 2
5 28 24
61 662 1320 720
1385 24568 83664 100800 40320
50521 1326122 6749040 13335840 11491200 3628800
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MAPLE
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A151775 := proc(n, k) if n= 0 then 1 ; else taylor( (tan(x))^(2*k)/cos(x), x=0, 2*n+1) ; diff(%, x$(2*n)) ; coeftayl(%, x=0, 0) ; fi; end: for n from 0 to 10 do for k from 0 to n do printf("%d ", A151775(n, k)) ; od: printf("\n") ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009]
T := proc (n, k) if n = 0 and k = 0 then 1 elif n = 0 then 0 else simplify(subs(x = 0, diff(tan(x)^(2*k)/cos(x), `$`(x, 2*n)))) end if end proc: for n from 0 to 7 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009]
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CROSSREFS
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A subtriangle of A008294.
Cf. A000364, A000281 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 27 2009]
Sequence in context: A002795 A127357 A025170 this_sequence A095159 A047132 A072371
Adjacent sequences: A151772 A151773 A151774 this_sequence A151776 A151777 A151778
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 24 2009, at the suggestion of Alexander R. Povolotsky
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EXTENSIONS
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More values from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 24 2009
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