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A003716 Expansion of tan(sinh(x)).
(Formerly M3144)
1
1, 3, 37, 1015, 47881, 3459819, 354711853, 48961863007, 8754050024209, 1967989239505875, 543326939019354421, 180718022989699819207, 71275877445849484090393, 32890432371345908634652347, 17555593768891213894861569085 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = sum(k=1..n, ((-1)^(k-1)+1)/(2^k*k!)*sum(i=0..k, (-1)^i*(k-2*i)^n *C(k,i))*(sum(j=1..k, j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j)))). - Vladimir Kruchinin, Apr 20 2011

a(n) ~ 4 * (2*n+1)! / (sqrt(4+Pi^2) * (log((Pi + sqrt(4+Pi^2))/2))^(2*n+2)). - Vaclav Kotesovec, Feb 16 2015

MATHEMATICA

Tan[ Sinh[ x ] ] (* Odd Part *)

nn = 20; Table[(CoefficientList[Series[Tan[Sinh[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)

PROG

(Maxima)

a(n):=sum(((-1)^(k-1)+1)/(2^k*k!)*sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k)*(sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k, j), j, 1, k)), k, 1, n); [Vladimir Kruchinin, Apr 20 2011]

CROSSREFS

Sequence in context: A003717 A201697 A274308 * A051396 A113074 A128083

Adjacent sequences:  A003713 A003714 A003715 * A003717 A003718 A003719

KEYWORD

nonn

AUTHOR

R. H. Hardin

STATUS

approved

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)