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A009733 Expansion of tan(x)*cosh(tan(x)). 0
1, 5, 81, 2477, 120481, 8496245, 817734321, 102873611549, 16372688411713, 3213260867586149, 761792907575450385, 214507625428065409805, 70732793117238811066081, 26987583518243293948764629 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = b(2*n-1), b(n) = Sum_{k=1..n} ((-1)^(k-1)+1)/(k-1)!*((-1)^(n-k)+1)*Sum_{j=k..n} binomial(j-1,k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)*stirling2(n,j). - Vladimir Kruchinin, Apr 21 2011

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Tan[x]Cosh[Tan[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jan 14 2015 *)

PROG

(Maxima)

a(n):=b(2*n-1);

b(n):=sum(((-1)^(k-1)+1)/(k-1)!*((-1)^(n-k)+1)*sum(binomial(j-1, k-1)*j!*2^(n-j-2)*(-1)^((n+k)/2+j)*stirling2(n, j), j, k, n), k, 1, n); /* Vladimir Kruchinin, Apr 21 2011 */

CROSSREFS

Sequence in context: A115032 A278883 A307376 * A009756 A336807 A188419

Adjacent sequences: A009730 A009731 A009732 * A009734 A009735 A009736

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Jan 14 2015

STATUS

approved

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Last modified February 1 08:20 EST 2023. Contains 359992 sequences. (Running on oeis4.)