A380308 Expansion of e.g.f. exp( 1 - 1/(1-2*x)^(1/2) ).

1, -1, -2, -7, -35, -226, -1769, -16003, -159998, -1669645, -16203509, -85724926, 2606965153, 154547040023, 6047755681150, 217270016433329, 7721994442008061, 279057037146008702, 10378357435103977207, 399487271346562859045, 15957215240554330744066

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..405

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * |Stirling1(n,k)| * A000587(k).

a(n) = e * (-2)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/2,n)/k!.

a(0) = 1; a(n) = -Sum_{k=1..n} A001147(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-2*x)^(1/2))))

Crossrefs

Cf. A145561, A380309, A380310.

Cf. A000587, A001147.

Sequence in context: A182224 A317421 A292182 * A185054 A014307 A000154

Adjacent sequences: A380305 A380306 A380307 * A380309 A380310 A380311

Keyword

sign

Author

Seiichi Manyama, Jan 20 2025

Status

approved