A054332 One half of tenth unsigned column of Lanczos triangle A053125 (decreasing powers).

5, 440, 16016, 366080, 6223360, 85995520, 1018716160, 10711072768, 102385254400, 905301196800, 7501067059200, 58822597017600, 439993025691648, 3158924287016960, 21879051958353920, 146801380881858560

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

References

• C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
• Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A053125, A054328.

Programs

GAP

List([0..20], n-> 2^(2*n-1)*Binomial(2*n+10, 9)); # G. C. Greubel, Jul 22 2019

Magma

[2^(2*n-1)*Binomial(2*n+10, 9): n in [0..20]]; // G. C. Greubel, Jul 22 2019

Mathematica

Table[2^(2*n-1)*Binomial[2*n+10,9], {n,0,20}] (* G. C. Greubel, Jul 22 2019 *)

PARI

vector(20, n, n--; 2^(2*n-1)*binomial(2*n+10, 9)) \\ G. C. Greubel, Jul 22 2019

Sage

[2^(2*n-1)*binomial(2*n+10, 9) for n in (0..20)] # G. C. Greubel, Jul 22 2019

Formula

a(n) = 2^(2*n-1)*binomial(2*n+10, 9) = -A053125(n+9, 9)/2 = A054328(n)/2.

G.f.: (1+40*x+80*x^2)*(5+40*x+16*x^2)/(1-4*x)^10.