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A000490
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Generalized Euler numbers c(4,n).
(Formerly M5027 N2169)
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6
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1, 16, 1280, 249856, 90767360, 52975108096, 45344872202240, 53515555843342336, 83285910482761809920, 165262072909347030040576, 407227428060372417275494400, 1219998300294918683087199010816, 4366953142363907901751614431559680, 18406538229888710811704852978971181056
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=0..13.
D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 689-694.
D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699.
D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]
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FORMULA
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a(n) = A000364(n)*16^n. - Philippe Deléham, Oct 27 2006
a(n) = (2*n)!*[x^(2*n)](sec(4*x)). - Peter Luschny, Nov 21 2021
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MAPLE
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egf := sec(4*x): ser := series(egf, x, 26):
seq((2*n)!*coeff(ser, x, 2*n), n = 0..11); # Peter Luschny, Nov 21 2021
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MATHEMATICA
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a0 = 4; nmax = 20; km0 = nmax; Clear[cc]; L[a_, s_, km_] := Sum[ JacobiSymbol[-a, 2*k+1]/(2*k+1)^s, {k, 0, km}]; c[a_, n_, km_] := 2^(2*n +1)*Pi^(-(2*n)-1)*(2*n)!*a^(2*n+1/2)*L[a, 2*n+1, km] // Round; cc[km_] := cc[km] = Table[c[a0, n, km], {n, 0, nmax}]; cc[km0]; cc[km = 2 km0]; While[cc[km] != cc[km/2, km = 2 km]]; A000490 = cc[km] (* Jean-François Alcover, Feb 05 2016 *)
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CROSSREFS
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Cf. A000187, A000436, A000318, A349264.
Sequence in context: A113104 A227602 A186856 * A308587 A027648 A224105
Adjacent sequences: A000487 A000488 A000489 * A000491 A000492 A000493
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 02 2000
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STATUS
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approved
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