A065954 - OEIS

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A065954

Nearest integer to (-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1)) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.

1, 1, 2, 3, 5, 9, 15, 26, 48, 87, 160, 296, 551, 1032, 1941, 3663, 6936, 13171, 25076, 47853, 91515, 175351, 336586, 647131, 1246070, 2402691, 4638908, 8967212, 17353538, 33618332, 65191863, 126535914, 245818071, 477938270, 929968028, 1810857391, 3528610690, 6880357956

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..37.

EXAMPLE

1, 1, 2, 3, 5, 17/2, 89/6, 211/8, 1903/40, 62473/720, ...

MATHEMATICA

e[n_, x_]:=Sum[(-x)^k/k!, {k, 0, n}]; a[n_]:=If[Denominator[num=(-1)^n*n!*(e[n, 2]-e[n, 1]e[n-1, 1])]==2, Round[num]+1, Round[num]]; Array[a, 38, 0] (* Stefano Spezia, Apr 12 2024 *)

CROSSREFS

Cf. A065952, A065953, A065955, A065956.

Sequence in context: A338192 A129852 A367666 * A067847 A190138 A273905

Adjacent sequences: A065951 A065952 A065953 * A065955 A065956 A065957

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 08 2001

EXTENSIONS

a(0)=1 prepended by and a(35)-a(37) from Stefano Spezia, Apr 12 2024

STATUS

approved