A375653 Expansion of e.g.f. exp(x^2 + x * exp(x^2)).

1, 1, 3, 13, 49, 321, 1891, 13693, 113793, 942049, 9428131, 93837261, 1043918833, 12318170593, 151123106499, 2024107965181, 27672074520961, 406722703307073, 6188268876372163, 98499148173678349, 1645657615850089521, 28317883192163927041

Offset: 0

Author

Seiichi Manyama, Aug 22 2024

Keywords

• nonn

Crossrefs

Cf. A216688, A375654.

Cf. A375604.

Programs

PARI

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

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k+1)^k/(k!*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^k / (k! * (n-2*k)!).