The On-Line Encyclopedia of Integer Sequences (OEIS)

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A300661

Expansion of e.g.f. exp(-Sum_{k>=1} prime(k)*x^k/k!).
(history; published version)

#8 by Alois P. Heinz at Thu Mar 15 18:14:34 EDT 2018

STATUS

editing

approved

#7 by Alois P. Heinz at Thu Mar 15 18:14:32 EDT 2018

LINKS

Alois P. Heinz, <a href="/A300661/b300661.txt">Table of n, a(n) for n = 0..542</a>

STATUS

approved

editing

#6 by Alois P. Heinz at Sat Mar 10 16:46:56 EST 2018

STATUS

editing

approved

#5 by Alois P. Heinz at Sat Mar 10 16:46:54 EST 2018

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, -add(a(n-j)*

ithprime(j)*binomial(n-1, j-1), j=1..n))

end:

seq(a(n), n=0..25); # Alois P. Heinz, Mar 10 2018

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Sat Mar 10 15:53:40 EST 2018

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Sat Mar 10 15:46:28 EST 2018

MATHEMATICA

a[n_] := a[n] = Sum[-Prime[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]

#2 by Ilya Gutkovskiy at Sat Mar 10 15:25:01 EST 2018

NAME

allocated for Ilya Gutkovskiy

Expansion of e.g.f. exp(-Sum_{k>=1} prime(k)*x^k/k!).

DATA

1, -2, 1, 5, 4, -53, -177, 282, 5759, 20355, -83420, -1420133, -6245485, 29035652, 648899541, 4034393367, -10488623858, -464971765297, -4310935438663, -3489419105786, 446500913437911, 6423072226704027, 30987397708208720, -462727554963927783, -11862200720684515159

OFFSET

0,2

LINKS

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

FORMULA

E.g.f.: exp(-Sum_{k>=1} A000040(k)*x^k/k!).

EXAMPLE

E.g.f.: A(x) = 1 - 2*x/1! + x^2/2! + 5*x^3/3! + 4*x^4/4! - 53*x^5/5! - 177*x^6/6! + 282*x^7/7! + ...

MATHEMATICA

nmax = 24; CoefficientList[Series[Exp[-Sum[Prime[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A000040, A007446, A007447, A030017, A030018, A300632.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Mar 10 2018

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Mar 10 15:25:01 EST 2018

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved