A360894 G.f. satisfies A(x) = 1 + x * A(x * (1 - x)).

1, 1, 1, 0, -2, -1, 7, 0, -44, 69, 276, -1471, 675, 20407, -90560, -20552, 2141700, -10558223, -675239, 329376824, -2106253225, 2364924062, 67114942438, -621638176430, 1926931098484, 14768396756732, -236623058229675, 1371752460097440, 1098671590491324

Offset

0,5

Links

Table of n, a(n) for n=0..28.

Formula

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\2, (-1)^j*binomial(i-1-j, j)*v[i-j])); v;

Crossrefs

Cf. A360896, A360897.

Cf. A127782.

Sequence in context: A063704 A224918 A224508 * A116891 A079620 A010254

Adjacent sequences: A360891 A360892 A360893 * A360895 A360896 A360897

Keyword

sign

Author

Seiichi Manyama, Feb 25 2023

Status

approved