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A255881 Expansion of exp( Sum_{n >= 1} A000364(n)*x^n/n ). 15
1, 1, 3, 23, 371, 10515, 461869, 28969177, 2454072147, 269732425859, 37312477130105, 6342352991066661, 1299300852841580893, 315702973949640373933, 89765549161833322593411, 29526682496433138896248775, 11124674379405792463701519059 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A000364(n) = (-1)^n*2^(2*n)*Euler(2*n,1/2), where E(n,x) is the n-th Euler polynomial. In general it appears that when k is a nonzero integer, the expansion of exp( Sum_{n >= 1} k^(2*n)*E(2*n,1/k)*(-x)^n/n ) has (positive) integer coefficients. See A255882 (k = 3), A255883(k = 4) and A255884 (k = 6).

LINKS

Table of n, a(n) for n=0..16.

E. W. Weisstein, Euler Polynomial

FORMULA

O.g.f.: exp( x + 5*x^2/2 + 61*x^3/3 + 1385*x^4/4 + ... ) = 1 + x + 3*x^2 + 23*x^3 + 371*x^4 + ....

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

MAPLE

#A255881

k := 2:

exp(add(k^(2*n)*euler(2*n, 1/k)*(-x)^n/n, n = 1 .. 16)): seq(coeftayl(%, x = 0, n), n = 0 .. 16);

CROSSREFS

Cf. A000364, A188514, A255882, A255883, A255884.

Sequence in context: A260509 A073588 A068338 * A243195 A233218 A114601

Adjacent sequences:  A255878 A255879 A255880 * A255882 A255883 A255884

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Mar 09 2015

STATUS

approved

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Last modified February 23 04:57 EST 2018. Contains 299473 sequences. (Running on oeis4.)