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A000318 Generalized tangent numbers d(4,n).
(Formerly M3713 N1517)
4
4, 128, 16384, 4456448, 2080374784, 1483911200768, 1501108249821184, 2044143848640217088, 3605459138582973251584, 7995891855149741436305408, 21776918737280678860353961984, 71454103701490016776039304265728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..100

D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 663-688.

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]

FORMULA

Equals 2^(4n-2) * A000182(n).

The g.f. has the following continued fraction expansion: g.f. = [4, b(0), c(0), b(1), c(1), b(2), c(2), ...] where b(n) = sum(k=0, n, 1/(2*k+1))^2 / (128*(n+1)*x), c(n) = -4/( sum(k=0, n, 1/(2*k+1))*sum(k=0, n+1, 1/(2*k+1))*(2*n+3) ) and each convergent of this continued fraction is a Pad'e approximant of the McLaurin series sum(k=1, \infty, a(n)*x^(n-1)). - Thomas Baruchel, Oct 19 2005

MATHEMATICA

nn = 30; t = Rest@Union[Range[0, nn - 1]! CoefficientList[Series[Tan[x], {x, 0, nn}], x]]; t2 = t*2^Range[2, 2*nn, 4] (* T. D. Noe, Jun 19 2012 *)

CROSSREFS

Cf. A000191.

Sequence in context: A267796 A013823 A130318 * A229385 A141367 A141368

Adjacent sequences:  A000315 A000316 A000317 * A000319 A000320 A000321

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000

STATUS

approved

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Last modified March 28 11:45 EDT 2017. Contains 284186 sequences.