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A101684 Exponent of 2 in denominators of expansion of e.g.f.: exp(-1 + sqrt(1+x)). 3
0, 1, 0, 3, 4, 3, 6, 7, 6, 9, 10, 8, 12, 13, 11, 15, 16, 15, 18, 19, 18, 21, 22, 19, 24, 25, 22, 27, 28, 27, 30, 31, 30, 33, 34, 32, 36, 37, 35, 39, 40, 39, 42, 43, 42, 45, 46, 42, 48, 49, 45, 51, 52, 51, 54, 55, 54, 57, 58, 56, 60, 61, 59, 63, 64, 63, 66, 67, 66, 69, 70, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
2^a(n) is denominator of c(n) where c(n) = (c(n-2) - (4*n-6)*c(n-1))/4, c(0) = 1, c(1) = 1/2. - Robert Israel, Nov 30 2023
MAPLE
S:= series(exp(-1+sqrt(1+x)), x, 201):
seq(padic:-ordp(denom(n!*coeff(S, x, n)), 2), n=0..200); # Robert Israel, Nov 30 2023
MATHEMATICA
IntegerExponent[Denominator[With[{nn=80}, CoefficientList[ Series[ Exp[ -1+Sqrt[1+x]], {x, 0, nn}], x] Range[0, nn]!]], 2] (* Harvey P. Dale, Aug 04 2021 *)
PROG
(PARI) my(x='x+O('x^30)); apply(x->(valuation(denominator(x), 2)), Vec(serlaplace(exp(sqrt(1+x)-1)))) \\ Michel Marcus, Nov 30 2023
CROSSREFS
First differences are in A101685. Cf. A101683.
Sequence in context: A074372 A331372 A049276 * A061800 A218789 A324335
KEYWORD
nonn
AUTHOR
Ralf Stephan, Dec 13 2004
EXTENSIONS
Definition clarified by Harvey P. Dale, Aug 04 2021
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)