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Expansion of e.g.f. log(1+x)*cosh(x).
4

%I #24 Apr 10 2022 13:28:23

%S 0,1,-1,5,-12,49,-225,1301,-8848,69441,-616185,6095429,-66475596,

%T 792143793,-10238194057,142633278997,-2130537219840,33964965659649,

%U -575573407212753,10331348137881349,-195807849389362540,3907452790559751857,-81892400673047263761,1798373345567005989781,-41294565798306731368272,989581607891834678407745

%N Expansion of e.g.f. log(1+x)*cosh(x).

%F a(n) ~ (n-1)! * (-1)^(n+1) * cosh(1). - _Vaclav Kotesovec_, Jan 23 2015

%F a(n) = -(-1)^n * Sum_{k=0..floor((n-1)/2)} binomial(n,2*k) * (n-2*k-1)!. - _Ilya Gutkovskiy_, Apr 10 2022

%t CoefficientList[Series[Cosh[x]*Log[1 + x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)

%Y Cf. A009410.

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997