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A238398 Numerators of inverse binomial transform of A198631(n)/A006519(n+1) with -1 instead of A198631(1)=1. 1
1, -3, 2, -11, 4, -11, 6, -39, 8, -49, 10, 647, 12, -5487, 14, 929329, 16, -3202325, 18, 221930505, 20, -4722116563, 22, 968383680643, 24, -14717667114201, 26, 2093660879252563, 28, -86125672563201239, 30, 129848163681107300961, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From modified fractional Euler numbers.

Inverse binomial transform:

1, -3/2, 2, -11/4, 4, -11/2, 6, -39/8, 8, -49/2, 10, 647/4, 12, -5487/2,... = a(n)/b(n).  b(2n) = A004277(n).

Difference table of c(n) = 1, -1/2, 0, -1/4,... :

1,    -1/2,    0,  -1/4,     0,    1/2,      0,...

-3/2,  1/2, -1/4,   1/4,   1/2,   -1/2,  -17/8,...

2,    -3/4,  1/2,   1/4,    -1,  -13/8,   17/4,...

-11/4, 5/4, -1/4,  -5/4,  -5/8,   47/8,   73/8,...

4,    -3/2,   -1,   5/8,  13/2,   13/4, -107/2,...

-11/2, 1/2, 13/8,  47/8, -13/4, -227/4, -227/8,

6,     9/8, 17/4, -73/8, -107/2, 227/8, 2957/4,...

etc.

c(n) + a(n)/b(n) = 2, -2, 2, -3, 4, -5, 6, -7, 8, -9,... = A233583(n+1) signed. (a(n) discovered in 2013)

LINKS

Table of n, a(n) for n=0..32.

MATHEMATICA

max = 40; (* b = A198631 *) b[0] = 1; b[1] = -1; b[n_] := Numerator[EulerE[n, 1]/(2^n-1)]; bb = Table[b[n]/2^IntegerExponent[n+1, 2], {n, 0, max}]; a[n_] := Differences[bb, n] // First // Numerator ; Table[a[n], {n, 0, max}]

CROSSREFS

Cf. A235774.

Sequence in context: A152177 A110326 A112061 * A065014 A013945 A072656

Adjacent sequences:  A238395 A238396 A238397 * A238399 A238400 A238401

KEYWORD

sign

AUTHOR

Paul Curtz, Feb 26 2014

STATUS

approved

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Last modified July 28 09:43 EDT 2021. Contains 346325 sequences. (Running on oeis4.)