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Expansion of e.g.f. exp(2*x^2 + x * exp(x^2)).
1

%I #9 Aug 23 2024 02:12:31

%S 1,1,5,19,97,641,4021,33475,272609,2559457,25926661,273419411,

%T 3221437825,38674360609,506595820277,6895149870211,98785254688321,

%U 1496456813264705,23400554985371269,386926938274889107,6593495476334628641,117506166655500705601

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

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

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

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

%Y Cf. A216688, A375653.

%Y Cf. A375627.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 22 2024