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A054330 One half of sixth unsigned column of Lanczos' triangle A053125. 2
3, 112, 2016, 25344, 256256, 2236416, 17547264, 127008768, 862912512, 5571084288, 34487664640, 206108098560, 1195426971648, 6757057298432, 37346888122368, 202396038856704, 1077912237244416, 5652245681012736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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 (24, -240, 1280, -3840, 6144, -4096).

FORMULA

a(n)= 2^(2*n-1)*binomial(2*n+6, 5) = -A053125(n+5, 5)/2 = A054324(n)/2.

G.f.: (4*x+3)*(12*x+1)/(1-4*x)^6.

E.g.f.: (90 + 3000*x + 17520*x^2 + 31680*x^3 + 20480*x^4 + 4096*x^5)* exp(4*x)/30. - G. C. Greubel, Jul 22 2019

MATHEMATICA

Table[2^(2*n-1)*Binomial[2*n+6, 5], {n, 0, 20}] (* G. C. Greubel, Jul 22 2019 *)

PROG

(PARI) vector(20, n, n--; 2^(2*n-1)*binomial(2*n+6, 5)) \\ G. C. Greubel, Jul 22 2019

(MAGMA) [2^(2*n-1)*Binomial(2*n+6, 5): n in [0..20]]; // G. C. Greubel, Jul 22 2019

(Sage) [2^(2*n-1)*binomial(2*n+6, 5) for n in (0..20)] # G. C. Greubel, Jul 22 2019

(GAP) List([0..20], n-> 2^(2*n-1)*Binomial(2*n+6, 5)); # G. C. Greubel, Jul 22 2019

CROSSREFS

Cf. A054324, A053125.

Sequence in context: A292336 A037116 A169996 * A024043 A199640 A221618

Adjacent sequences:  A054327 A054328 A054329 * A054331 A054332 A054333

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)