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A300622 Denominators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, ... (1 with primes). 1
1, 1, 2, 1, 4, 4, 8, 4, 16, 16, 32, 16, 64, 64, 128, 64, 256, 256, 512, 256, 1024, 1024, 2048, 1024, 4096, 4096, 8192, 4096, 16384, 16384, 32768, 16384, 65536, 65536, 131072, 65536, 262144, 262144, 524288, 262144, 1048576, 1048576, 2097152, 1048576, 4194304, 4194304, 8388608, 4194304 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..47.

N. J. A. Sloane, Transforms

FORMULA

Denominators of coefficients in expansion of e.g.f. sqrt(1 + Sum_{k>=1} prime(k)*x^k/k!).

Empirical g.f.: (1 + x*(1 + x)^2)/(1 - 4*x^4).

EXAMPLE

1, 1, 1/2, 1, -5/4, 27/4, -277/8, 895/4, -27655/16, 248185/16, -5052519/32, 28731489/16, -1444496477/64, 19885473347/64, ...

MATHEMATICA

Denominator[nmax = 47; CoefficientList[Series[(1 + Sum[Prime[k] x^k/k!, {k, 1, nmax}])^(1/2), {x, 0, nmax}], x] Range[0, nmax] !]

CROSSREFS

Cf. A008578, A073749, A073750, A300621 (numerators).

Sequence in context: A296188 A008312 A060723 * A195691 A074763 A099932

Adjacent sequences:  A300619 A300620 A300621 * A300623 A300624 A300625

KEYWORD

nonn,frac

AUTHOR

Ilya Gutkovskiy, Aug 14 2018

STATUS

approved

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)