|
| |
|
|
A053130
|
|
Binomial coefficients C(2*n-7,8).
|
|
6
|
|
|
|
9, 165, 1287, 6435, 24310, 75582, 203490, 490314, 1081575, 2220075, 4292145, 7888725, 13884156, 23535820, 38608020, 61523748, 95548245, 145008513, 215553195, 314457495, 450978066, 636763050, 886322710, 1217566350
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
8,1
|
|
|
COMMENTS
|
a(n)= A053123(n,8), n >= 8; a(n) := 0, n=0..7,(ninth column of shifted Chebyshev's S-triangle, decreasing order)
|
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 8..200
Milan Janjic, Two Enumerative Functions
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Chebyshev polynomials.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
|
|
|
FORMULA
|
a(n) = binomial(2*n-7, 8) if n >= 8 else 0.
G.f.: (9+84*x+126*x^2+36*x^3+x^4)/(1-x)^9.
|
|
|
MATHEMATICA
|
Table[Binomial[2*n-7, 8], {n, 8, 50}] (* G. C. Greubel, Aug 26 2018 *)
|
|
|
PROG
|
(MAGMA) [Binomial(2*n-7, 8): n in [8..50]]; // Vincenzo Librandi, Apr 07 2011
(PARI) for(n=8, 50, print1(binomial(2*n-7, 8), ", ")) \\ G. C. Greubel, Aug 26 2018
|
|
|
CROSSREFS
|
Cf. A053123, A053129.
Sequence in context: A041144 A212334 A086759 * A219074 A166180 A004107
Adjacent sequences: A053127 A053128 A053129 * A053131 A053132 A053133
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Wolfdieter Lang
|
|
|
STATUS
|
approved
|
| |
|
|
