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A054329 One quarter of fourth unsigned column of Lanczos' triangle A053125. 2
1, 20, 224, 1920, 14080, 93184, 573440, 3342336, 18677760, 100925440, 530579456, 2726297600, 13740539904, 68115496960, 332859965440, 1606317768704, 7666516623360, 36232344109056, 169737107537920, 788899592929280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256).

FORMULA

a(n)= 4^(n-1)*binomial(2*n+4, 3)= -A053125(n+3, 3)/4 = A054322(n)/4.

G.f.: (1+4*x)/(1-4*x)^4.

E.g.f.: (3 + 48*x + 120*x^2 + 64*x^3)*exp(4*x)/3. - G. C. Greubel, Jul 22 2019

MATHEMATICA

Table[4^(n-1)*Binomial[2*n+4, 3], {n, 0, 30}] (* G. C. Greubel, Jul 22 2019 *)

PROG

(PARI) vector(30, n, n--; 4^(n-1)*binomial(2*n+4, 3)) \\ G. C. Greubel, Jul 22 2019

(MAGMA) [4^(n-1)*Binomial(2*n+4, 3): n in [0..30]]; // G. C. Greubel, Jul 22 2019

(Sage) [4^(n-1)*binomial(2*n+4, 3) for n in (0..30)] # G. C. Greubel, Jul 22 2019

(GAP) List([0..30], n-> 4^(n-1)*Binomial(2*n+4, 3)); # G. C. Greubel, Jul 22 2019

CROSSREFS

Cf. A054322, A053125.

Sequence in context: A000833 A302661 A178261 * A112503 A007160 A195265

Adjacent sequences:  A054326 A054327 A054328 * A054330 A054331 A054332

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)