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A054331 One eighth of eighth unsigned column of Lanczos' triangle A053125. 2
1, 60, 1584, 27456, 366080, 4073472, 39690240, 349274112, 2835283968, 21554790400, 155194490880, 1067345510400, 7058711642112, 45127489814528, 280101660917760, 1693862087098368, 10009185060126720, 57935518230380544 (list; table; 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.

FORMULA

a(n) = 2^(2*n-3)*binomial(2*n+8, 7) = -A053125(n+7, 7)/8 = A054326(n)/8.

G.f. (1+4*x)*(1+24*x+16*x^2)/(1-4*x)^8.

MATHEMATICA

Table[4^n Binomial[2n+8, 7]/8, {n, 0, 20}] (* Harvey P. Dale, Nov 03 2011 *)

PROG

(PARI) vector(20, n, n--; 2^(2*n-3)*binomial(2*n+8, 7)) \\ G. C. Greubel, Jul 22 2019

(MAGMA) [2^(2*n-3)*Binomial(2*n+8, 7): n in [0..20]]; // G. C. Greubel, Jul 22 2019

(Sage) [2^(2*n-3)*binomial(2*n+8, 7) for n in (0..20)] # G. C. Greubel, Jul 22 2019

(GAP) List([0..20], n-> 2^(2*n-3)*Binomial(2*n+8, 7)); # G. C. Greubel, Jul 22 2019

CROSSREFS

Cf. A054326, A053125.

Sequence in context: A289156 A288960 A269196 * A160349 A281373 A053528

Adjacent sequences:  A054328 A054329 A054330 * A054332 A054333 A054334

KEYWORD

easy,nice,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 14 15:10 EST 2019. Contains 329126 sequences. (Running on oeis4.)