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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
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.
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
Sequence in context: A292336 A037116 A169996 * A024043 A199640 A221618
KEYWORD
easy,nonn
STATUS
approved