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A009596 Expansion of e.g.f. sinh(sin(x)^2) (even powers only). 3
0, 2, -8, 152, -6848, 312992, -17468288, 1385712512, -143250864128, 17321985331712, -2418583050119168, 396575082357512192, -75839817371814084608, 16517549362496506929152 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 8*Sum_{j=1..n} 2^(2*n-4*j)/(2*j-1)!*Sum_{i=0..2*j-1} (i-2*j+1)^(2*n)*binomial(4*j-2,i)*(-1)^(n-1-i). - Vladimir Kruchinin, Jun 08 2011
EXAMPLE
sinh(sin(x)*sin(x)) = 2/2!*x^2 - 8/4!*x^4 + 152/6!*x^6 - 6848/8!*x^8... - Patrick Demichel (patrick.demichel(AT)hp.com)
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Sinh[Sin[x]^2], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 30 2018 *)
PROG
(Maxima)
a(n):=8*sum(2^(2*n-4*j)/(2*j-1)!*sum((i-2*j+1)^(2*n)*binomial(4*j-2, i)*(-1)^(n-1-i), i, 0, 2*j-1), j, 1, n); /* Vladimir Kruchinin, Jun 08 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(sin(x)^2))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 30 2018
CROSSREFS
Sequence in context: A007314 A102099 A012298 * A012571 A018926 A012432
KEYWORD
sign
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)