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URL: https://oeis.org/A321632

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A321632
Expansion of e.g.f. (1 + sin(x))/exp(x).
1
1, 0, -1, 1, 1, -5, 9, -9, 1, 15, -31, 31, 1, -65, 129, -129, 1, 255, -511, 511, 1, -1025, 2049, -2049, 1, 4095, -8191, 8191, 1, -16385, 32769, -32769, 1, 65535, -131071, 131071, 1, -262145, 524289, -524289, 1, 1048575, -2097151, 2097151, 1, -4194305, 8388609, -8388609
OFFSET
0,6
COMMENTS
A140323(n) = |a(4*n-1)| = |a(4*n-2)|, A247281(n) = |a(4*n+1)|.
The absolute values of the coefficients of the expansion of the reciprocal of this function are listed in A186364.
FORMULA
a(4*k) = 1;
a(4*k+1) = (-4)^k - 1;
a(4*k+2) = -2*a(4*k+1) - 1 = -2*(-4)^k + 1;
a(4*k+3) = 2*a(4*k+1) + 1 = 2*(-4)^k - 1.
From Colin Barker, Nov 16 2018: (Start)
G.f.: (1 + 3*x + 3*x^2) / ((1 + x)*(1 + 2*x + 2*x^2)).
a(n) = (-1)^n + i/2*((-1-i)^n - (-1+i)^n), where i=sqrt(-1).
a(n) = -3*a(n-1) - 4*a(n-2) - 2*a(n-3) for n>2. (End)
MAPLE
seq(factorial(n)*coeff(series((1+sin(x))/exp(x), x=0, 48), x, n), n=0..47);
MATHEMATICA
With[{nn=50}, CoefficientList[Series[(1+Sin[x])/Exp[x], {x, 0, nn}], x] Range[ 0, nn]!] (* or *) LinearRecurrence[{-3, -4, -2}, {1, 0, -1}, 50] (* Harvey P. Dale, Jul 21 2021 *)
PROG
(PARI) Vec((1 + 3*x + 3*x^2) / ((1 + x)*(1 + 2*x + 2*x^2)) + O(x^40)) \\ Colin Barker, Nov 16 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paolo P. Lava, Nov 16 2018
STATUS
approved