A173590 - OEIS

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A173590

T(n, k) = k^n*U(n, (1/k + k)/2) + (n + 1)^(k - 1)*U(k - 1, (1/(n + 1) + n + 1)/2), where U(n,x) is the n-th Chebyshev polynomial of the second kind, square array read by antidiagonals (n >= 0, k >= 1).

2

2, 3, 3, 4, 10, 4, 5, 31, 31, 5, 6, 102, 182, 102, 6, 7, 367, 1093, 1093, 367, 7, 8, 1402, 8032, 8738, 8032, 1402, 8, 9, 5511, 67763, 86181, 86181, 67763, 5511, 9, 10, 21910, 600322, 1166470, 813802, 1166470, 600322, 21910, 10, 11, 87463, 5385001, 18015797, 11900131, 11900131, 18015797, 5385001, 87463, 11

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = A173588(n,k) + A173588(k-1,n+1).

EXAMPLE

Square array begins:

n\k | 1 2 3 4 5 6 ...

-----------------------------------------------------

0 | 2 3 4 5 6 7 ...

1 | 3 10 31 102 367 1402 ...

2 | 4 31 182 1093 8032 67763 ...

3 | 5 102 1093 8738 86181 1166470 ...

4 | 6 367 8032 86181 813802 11900131 ...

5 | 7 1402 67763 1166470 11900131 124387562 ...

6 | 8 5511 600322 18015797 260198052 2527336267 ...

...

MATHEMATICA

p[x_, q_] = 1/(x^2 - (1/q + q)*x + 1);

a = Table[Table[n^m*SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 1, 21}];

b = (a + Transpose[a]);

Flatten[Table[Table[b[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]

PROG

(Maxima)

T(n, k) := k^n*chebyshev_u(n, (1/k + k)/2) + (n + 1)^(k - 1)*chebyshev_u(k - 1, (1/(n + 1) + n + 1)/2)$

create_list(T(n - k + 1, k), n, 0, 12, k, 1, n + 1);

/* Franck Maminirina Ramaharo, Jan 24 2019 */

CROSSREFS

Cf. A173588, A173591.

Sequence in context: A227263 A111574 A330510 * A128744 A293984 A207608

Adjacent sequences: A173587 A173588 A173589 * A173591 A173592 A173593

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula, Feb 22 2010

EXTENSIONS

Edited by Franck Maminirina Ramaharo, Jan 24 2019

STATUS

approved