A300622 Denominators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, ... (1 with primes).

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

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: A008312 A345442 A060723 * A195691 A074763 A099932

Adjacent sequences: A300619 A300620 A300621 * A300623 A300624 A300625

Keyword

nonn,frac

Author

Ilya Gutkovskiy, Aug 14 2018

Status

approved