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A256978 Irregular triangle read by rows: coefficients of polynomials related to Stirling permutations. 0
1, 1, 1, 1, 1, 3, 7, 3, 1, 1, 7, 29, 31, 29, 7, 1, 1, 15, 101, 195, 321, 195, 101, 15, 1, 1, 31, 327, 1001, 2507, 2661, 2507, 1001, 327, 31, 1, 1, 63, 1023, 4641, 16479, 26481, 37759, 26481, 16479, 4641, 1023, 63, 1, 1, 127, 3145, 20343, 98289, 221775, 439105, 461455, 439105, 221775, 98289, 20343, 3145, 127, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..64.

Shi-Mei Ma and Toufik Mansour, The 1/k-Eulerian polynomials and k-Stirling permutations, arXiv preprint, arXiv:1409.6525 [math.CO], 2014. See polynomials C_n(x).

Shi-Mei Ma and Toufik Mansour, The 1/k-Eulerian polynomials and k-Stirling permutations, Discrete Mathematics, Volume 338, Issue 8, 2015, 1468-1472.

Shi-Mei Ma, Yeong-Nan Yeh, The alternating run polynomials of permutations, arXiv:1904.11437 [math.CO], 2019. See p. 9.

FORMULA

E.g.f.: (exp(z*(x - 1)*(x + 1)) + x)/(x + 1)*sqrt((1 - x^2)/(exp(2*z*(x - 1)*(x + 1)) - x^2)) - 1. - Franck Maminirina Ramaharo, Feb 05 2019

EXAMPLE

Triangle begins:

  n\k | 1   2   3    4    5    6    7    8   9  10  11

  ----+-----------------------------------------------

    1 | 1

    2 | 1   1   1

    3 | 1   3   7    3    1

    4 | 1   7  29   31   29    7    1

    5 | 1  15 101  195  321  195  101   15   1

    6 | 1  31 327 1001 2507 2661 2507 1001 327  31   1

    ...

PROG

(Maxima)

gf : taylor((exp(z*(x - 1)*(x + 1)) + x)/(x + 1)*sqrt((1 - x^2)/(exp(2*z*(x - 1)*(x + 1)) - x^2)) - 1, z, 0, 50)$

row(x, n) := n!*ratcoef(gf, z, n)$

create_list(ratcoef(row(x, n), x, k), n, 1, 20, k, 1, hipow(row(x, n), x));

/* Franck Maminirina Ramaharo, Feb 05 2019 */

CROSSREFS

Cf. A185410.

Sequence in context: A133368 A153027 A161127 * A296442 A021272 A135613

Adjacent sequences:  A256975 A256976 A256977 * A256979 A256980 A256981

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 23 2015

EXTENSIONS

More terms from Franck Maminirina Ramaharo, Feb 05 2019

STATUS

approved

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Last modified February 21 20:20 EST 2020. Contains 332110 sequences. (Running on oeis4.)