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A255900 Expansion of exp( Sum_{n >= 1} A000464(n-1)*x^n/n ). 1
1, 1, 6, 126, 6291, 581499, 86010084, 18599726484, 5532984567639, 2166830287921959, 1080602568966548022, 668603866168566179982, 502601850887023486736757, 451167540495577093495790397, 476690705981608679350490956032, 585587125411920596898761442409728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For similar results see A188514 and A255881.

A000464(n-1) = (-1)^n*4^(2*n-1)*E(2*n-1,1/4), where E(n,x) denotes the n-th Euler polynomial.

More generally, calculation suggests that for integer h and a nonzero integer k the expansion of exp ( Sum_{n >= 1} (2*k)^(2*n-1)*E(2*n-1,h/(2*k)) )*x^n/n has integer coefficients. This is the case h = 1 and k = 2.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..200

FORMULA

O.g.f.: exp( x + 11*x^2/2 + 361*x^3/3 + 24611*x^4/4 + ... ) = 1 + x + 6*x^2 + 126*x^3 + 6291*x^4 + ....

a(0) = 1 and a(n) = 1/n*Sum_{k = 1..n} (-1)^k*4^(2*k-1)*E(2*k-1,1/4)*a(n-k) for n >= 1.

MAPLE

#A255900

k := 2:

exp(add((2*k)^(2*n-1)*euler(2*n-1, 1/(2*k))*(-x)^n/n, n = 1 .. 15)): seq(coeftayl(%, x = 0, n), n = 0 .. 15);

MATHEMATICA

A000464:= With[{nn = 200}, Take[CoefficientList[Series[Sin[x]/Cos[2 x], {x, 0, nn}], x]*Range[0, nn-1]!, {2, -1, 2}]]; a:= With[{nmax = 50}, CoefficientList[Series[Exp[x + Sum[A000464[[k]]*x^(k)/(k), {k, 2, 75}]], {x, 0, nmax}], x]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 26 2018 *)

CROSSREFS

Cf. A000464, A188514, A255881.

Sequence in context: A228290 A004993 A237428 * A133792 A081623 A223210

Adjacent sequences:  A255897 A255898 A255899 * A255901 A255902 A255903

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Mar 10 2015

STATUS

approved

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Last modified January 28 03:39 EST 2020. Contains 331317 sequences. (Running on oeis4.)