A337062 E.g.f.: exp(1 + x^2/2 - exp(x)).

1, -1, 1, -2, 4, -7, 21, -51, 113, -498, 1088, -3335, 21407, -14653, 232389, -1275288, -3636526, -44468245, -7468609, 700603965, 12178055777, 67189448344, 175549544778, -2432123216941, -36279392911507, -287078642854853, -945866835928323

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(0) = 1; a(n) = -a(n-1) - Sum_{k=3..n} binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * (2*k-1)!! * A000587(n-2*k).

Mathematica

nmax = 26; CoefficientList[Series[Exp[1 + x^2/2 - Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[Binomial[n - 1, k - 1] a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 26}]
Table[Sum[Binomial[n, 2 k] (2 k - 1)!! BellB[n - 2 k, -1], {k, 0, Floor[n/2]}], {n, 0, 26}]

Crossrefs

Cf. A000587, A001147, A097514, A293037, A293038.

Sequence in context: A188497 A237759 A306978 * A153550 A102984 A103017

Adjacent sequences: A337059 A337060 A337061 * A337063 A337064 A337065

Keyword

sign

Author

Ilya Gutkovskiy, Aug 13 2020

Status

approved