A367486 Expansion of e.g.f. 1/(3 - 2*exp(x))^x.

1, 0, 4, 18, 168, 1830, 24540, 388122, 7084560, 146650446, 3395460900, 86962122786, 2441210321880, 74542218945558, 2459830123779756, 87236196407090730, 3308881779086345760, 133667058288336876894, 5729380391745420070068

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A367489(k) * binomial(n-1,k-1) * a(n-k).

Prog

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

Crossrefs

Cf. A004123, A367470, A367471.

Cf. A354413, A367488.

Cf. A367489.

Sequence in context: A302827 A007153 A239839 * A156870 A240317 A145075

Adjacent sequences: A367483 A367484 A367485 * A367487 A367488 A367489

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved