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 A280794 E.g.f.: cosh( Integral exp(x^2) dx )^2. 2

%I

%S 1,2,24,576,22656,1302528,101763072,10295230464,1303603347456,

%T 201345802960896,37165722291929088,8062848653812826112,

%U 2027520921133859733504,584153907885564625944576,190935313631330908457926656,70201900206284691681897873408,28820073606162151615036529836032

%N E.g.f.: cosh( Integral exp(x^2) dx )^2.

%H G. C. Greubel, <a href="/A280794/b280794.txt">Table of n, a(n) for n = 0..250</a>

%F E.g.f.: ( cosh( Integral 2*exp(x^2) dx ) + 1 ) / 2.

%F E.g.f.: cosh( sqrt(Pi)/2 * i * erf(i*x) )^2.

%F E.g.f.: ( cosh( sqrt(Pi) * i * erf(i*x) ) + 1 )/ 2.

%e E.g.f.: A(x) = 1 + 2*x^2/2! + 24*x^4/4! + 576*x^6/6! + 22656*x^8/8! + 1302528*x^10/10! + 101763072*x^12/12! + 10295230464*x^14/14! + 1303603347456*x^16/16! + 201345802960896*x^18/18! + 37165722291929088*x^20/20! +...

%e RELATED SERIES.

%e Integral exp(x^2) dx = x + 2*x^3/3! + 12*x^5/5! + 120*x^7/7! + 1680*x^9/9! + 30240*x^11/11! + 665280*x^13/13! +...+ A001813(n-1)*x^(2*n-1)/(2*n-1)! +...

%e Cosh( Integral exp(x^2) dx ) = 1 + x^2/2! + 9*x^4/4! + 153*x^6/6! + 4209*x^8/8! + 172689*x^10/10! + 9918009*x^12/12! +...+ A279840(2*n)*x^(2*n)/(2*n)! +...

%e Sinh( Integral exp(x^2) dx ) = x + 3*x^3/3! + 33*x^5/5! + 723*x^7/7! + 25377*x^9/9! + 1269699*x^11/11! +...+ A279840(2*n+1)*x^(2*n+1)/(2*n+1)! +...

%e Coefficients a(n) divided by 2^n begin:

%e [1, 1, 6, 72, 1416, 40704, 1590048, 80431488, 5092200576, 393253521408, 36294650675712, 3936937819244544, ...].

%t With[{nn = 50}, CoefficientList[Series[Cosh[Sqrt[Pi]/2*I*Erf[I*x]]^2, {x, 0, nn}], x] Range[0, nn]!][[;; ;; 2]] (* _G. C. Greubel_, Apr 11 2017 *)

%o (PARI) {a(n) = (2*n)!*polcoeff( cosh( intformal( exp(x^2 +x*O(x^(2*n)) ) ) )^2, 2*n)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A279840, A001813.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 23 2017

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)