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A198895 Triangle of coefficients arising in expansion of n-th derivative of tan(x) + sec(x). 0
1, 1, 1, 1, 2, 1, 1, 4, 5, 2, 1, 8, 18, 16, 5, 1, 16, 58, 88, 61, 16, 1, 32, 179, 416, 479, 272, 61, 1, 64, 543, 1824, 3111, 2880, 1385, 272, 1, 128, 1636, 7680, 18270, 24576, 19028, 7936, 1385, 1, 256, 4916, 31616, 101166, 185856, 206276 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..51.

Shi-Mei Ma, Derivative polynomials and permutations by numbers of interior peaks and left peaks, 2011. arXiv:1106.5781

FORMULA

n-th row represents the coefficients of the polynomial R_n(x) defined by the recurrence: R_0(x) = 1, R_1(x) = 1+x, and for n>=1, R_{n+1}(x) = (1+n*x^2)*R_n(x) + x*(1-x^2)*R'_n(x).

EXAMPLE

Triangle begins

1

1 1

1 2 1

1 4 5 2

1 8 18 16 5

1 16 58 88 61 16

1 32 179 416 479 272 61

...

CROSSREFS

Cf. A098558 (row sums?), A000111 (diagonal and 1st subdiagonal), A000340 (column 3) A000431 (column 4), A000363 (column 5)

Sequence in context: A263284 A158471 A158472 * A118686 A102610 A203300

Adjacent sequences:  A198892 A198893 A198894 * A198896 A198897 A198898

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 31 2011

EXTENSIONS

More terms from Max Alekseyev, Feb 17 2012

STATUS

approved

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Last modified June 24 22:04 EDT 2019. Contains 324337 sequences. (Running on oeis4.)