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A296729 Expansion of e.g.f. arcsin(x*cosh(x)) (odd powers only). 4
1, 4, 44, 1912, 156816, 21506816, 4420845376, 1271132964480, 487161448339712, 239980527068474368, 147742478026391141376, 111153314734461183924224, 100339775128577885016985600, 107037870347952811373977239552, 133204585741561810426003651444736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x*cosh(x)).

EXAMPLE

arcsin(x*cosh(x)) = x/1! + 4*x^3/3! + 44*x^5/5! + 1912*x^7/7! + 156816*x^9/9! + ...

MATHEMATICA

nmax = 15; Table[(CoefficientList[Series[ArcSin[x Cosh[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

PROG

(PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asin(x*cosh(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017

CROSSREFS

Cf. A001818, A009015, A009016, A009446, A009447, A009633, A009634, A012495, A012780, A101928, A191512, A296464, A296466, A296679, A296680, A296728, A296730, A296731, A296740.

Sequence in context: A217473 A127635 A134174 * A157193 A224784 A243221

Adjacent sequences:  A296726 A296727 A296728 * A296730 A296731 A296732

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 19 2017

STATUS

approved

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Last modified August 21 06:54 EDT 2019. Contains 326162 sequences. (Running on oeis4.)