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A009569 Expansion of e.g.f. sinh(log(1+tan(x))). 2
0, 1, -1, 5, -20, 136, -976, 8840, -88640, 1019776, -12933376, 181318400, -2767631360, 45821372416, -816582578176, 15596531778560, -317710534983680, 6876972491309056, -157606194409701376, 3812752893951672320, -97090584769337753600, 2596013487025352605696 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..430

FORMULA

a(n) ~ n! * (-1)^(n+1) * 4^n / Pi^(n+1). - Vaclav Kotesovec, Jan 23 2015

MATHEMATICA

CoefficientList[Series[(Tan[x]*(2 + Tan[x]))/(2*(1 + Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Tan[x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 21 2018 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+tan(x)))))) \\ G. C. Greubel, Jan 21 2018

CROSSREFS

Sequence in context: A081067 A318250 A024066 * A061964 A133667 A318433

Adjacent sequences:  A009566 A009567 A009568 * A009570 A009571 A009572

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

Terms a(20) and a(21) added by G. C. Greubel, Jan 21 2018

STATUS

approved

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Last modified October 19 11:27 EDT 2018. Contains 316358 sequences. (Running on oeis4.)