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A054324 Sixth unsigned column of Lanczos triangle A053125 (decreasing powers). 3
6, 224, 4032, 50688, 512512, 4472832, 35094528, 254017536, 1725825024, 11142168576, 68975329280, 412216197120, 2390853943296, 13514114596864, 74693776244736, 404792077713408, 2155824474488832, 11304491362025472 (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
Index entries for linear recurrences with constant coefficients, signature (24, -240, 1280, -3840, 6144, -4096).
FORMULA
a(n) = 4^n*binomial(2*n+6, 5) = -A053125(n+5, 5)= 2*A054330(n).
G.f.: 2*(3+4*x)*(1+12*x)/(1-4*x)^6.
E.g.f.: (2/15)*(45 +1500*x +8760*x^2 +15840*x^3 +10240*x^4 +2048*x^5) * exp(4*x). - G. C. Greubel, Jul 22 2019
MATHEMATICA
Table[4^n Binomial[2n+6, 5], {n, 0, 20}] (* or *) LinearRecurrence[{24, -240, 1280, -3840, 6144, -4096}, {6, 224, 4032, 50688, 512512, 4472832}, 20] (* Harvey P. Dale, Jul 02 2017 *)
PROG
(PARI) vector(20, n, n--; 4^n*binomial(2*n+6, 5)) \\ G. C. Greubel, Jul 22 2019
(Magma) [4^n*Binomial(2*n+6, 5): n in [0..20]]; // G. C. Greubel, Jul 22 2019
(Sage) [4^n*binomial(2*n+6, 5) for n in (0..20)] # G. C. Greubel, Jul 22 2019
(GAP) List([0..20], n-> 4^n*Binomial(2*n+6, 5)); # G. C. Greubel, Jul 22 2019
CROSSREFS
Sequence in context: A144045 A355669 A061610 * A117255 A130644 A223100
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)