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A054331
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One eighth of eighth unsigned column of Lanczos' triangle A053125.
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2
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1, 60, 1584, 27456, 366080, 4073472, 39690240, 349274112, 2835283968, 21554790400, 155194490880, 1067345510400, 7058711642112, 45127489814528, 280101660917760, 1693862087098368, 10009185060126720, 57935518230380544
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listen;
history;
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internal format)
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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Table[4^n Binomial[2n+8, 7]/8, {n, 0, 20}] (* Harvey P. Dale, Nov 03 2011 *)
LinearRecurrence[{32, -448, 3584, -17920, 57344, -114688, 131072, -65536}, {1, 60, 1584, 27456, 366080, 4073472, 39690240, 349274112}, 20] (* Harvey P. Dale, Feb 25 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nice,nonn
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AUTHOR
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STATUS
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approved
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