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A009277
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E.g.f. exp(tanh(x)^2) (even powers only).
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2
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1, 2, -4, -88, 4496, -155488, 675776, 903834752, -178181918464, 26154843525632, -2632795710260224, -207121926659381248, 274561534481040183296, -132684091405061956722688, 50873850498309673207709696
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{m=1..n} (Sum_{k=0..2*n-2*m} (binomial(k+2*m-1, 2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, k+2*m))/m!). - Vladimir Kruchinin, Jun 06 2011
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MATHEMATICA
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nmax = 20; Table[(CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}] (* Vaclav Kotesovec, May 27 2022 *)
With[{nn=30}, Take[CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Apr 08 2023 *)
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PROG
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(Maxima) a(n):=sum(sum(binomial(k+2*m-1, 2*m-1)*(k+2*m)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, k+2*m), k, 0, 2*n-2*m)/m!, m, 1, n); /* Vladimir Kruchinin, Jun 06 2011 */
(PARI) x = 'x + O(x^50); select(x->x, Vec(serlaplace(exp(tanh(x)^2)))) \\ Michel Marcus, Apr 01 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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