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A001250
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Coefficient of x^n/n! in power series expansion of (tan x + sec x)^2.
(Formerly M1235 N0472)
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6
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1, 2, 4, 10, 32, 122, 544, 2770, 15872, 101042, 707584, 5405530, 44736512, 398721962, 3807514624, 38783024290, 419730685952, 4809759350882, 58177770225664, 740742376475050, 9902996106248192, 138697748786275802
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 262.
C. Davis, Problem 4755, Amer. Math. Monthly, 65 (1958), 533-534.
S. Kitaev, Multi-avoidance of generalized patterns, Discrete Math., 260 (2003), 89-100. (See p. 100.)
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Alternating Permutation
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FORMULA
| Coefficient of x^n/n! in power series expansion of 2 * (tan x + sec x) is a(n-1) if n>1. - Michael Somos Feb 05 2011
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PROG
| (PARI) {a(n) = local(v=[1], t); if( n<0, 0, for(k=2, n+3, t=0; v = vector(k, i, if( i>1, t += v[k+1 - i]))); v[3])} /* Michael Somos Feb 03 2004 */
(PARI) {a(n) = if( n<0, 0, n! * polcoeff( (tan(x + x * O(x^n)) + 1 / cos(x + x * O(x^n)))^2, n))} /* Michael Somos Feb 05 2011 */
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CROSSREFS
| Apart from initial term, twice A000111. A diagonal of A010094.
Sequence in context: A120017 A000736 A176006 * A013032 A098830 A121277
Adjacent sequences: A001247 A001248 A001249 * A001251 A001252 A001253
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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