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, 957545370752122880, 6089666693993332736, 37854684854553149440

Offset

0,1

References

Cornelius Lanczos, Applied Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.

Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2nd ed., Wiley, New York, 1990.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (40,-720,7680,-53760,258048,-860160,1966080,-2949120,2621440,-1048576).

Index entries for sequences related to Chebyshev polynomials.

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.

From Amiram Eldar, Oct 30 2025: (Start)

Sum_{n>=0} 1/a(n) = 3351057/35 + 236232*log(2) - 236196*log(3).

Sum_{n>=0} (-1)^n/a(n) = -244401/35 + 24192*arctan(1/2) - 18972*log(5/4). (End)

Mathematica

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

Prog

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

Crossrefs

Cf. A053125, A054328.

Sequence in context: A038003 A359992 A377724 * A145247 A317345 A333263

Adjacent sequences: A054329 A054330 A054331 * A054333 A054334 A054335

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved