A375654 Expansion of e.g.f. exp(2*x^2 + x * exp(x^2)).

1, 1, 5, 19, 97, 641, 4021, 33475, 272609, 2559457, 25926661, 273419411, 3221437825, 38674360609, 506595820277, 6895149870211, 98785254688321, 1496456813264705, 23400554985371269, 386926938274889107, 6593495476334628641, 117506166655500705601

Offset: 0

Author

Seiichi Manyama, Aug 22 2024

Keywords

• nonn

Crossrefs

Cf. A216688, A375653.

Cf. A375627.

Programs

PARI

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

PARI

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

Formula

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