A380752 - OEIS

%I #8 Feb 01 2025 08:42:23

%S 1,3,41,1114,46217,2595186,184264033,15839938318,1599772132337,

%T 185698542344050,24362771800087241,3565209717372983142,

%U 575786158331135496313,101729690893078619387914,19518889966696995273600209,4041785999884112498658681406,898403694387449768732923267937

%N E.g.f. A(x) satisfies A(x) = exp(x * A(x)) / (1 - x * A(x)^2)^2.

%F a(n) = n! * Sum_{k=0..n} (2*n-k+1)^(k-1) * binomial(5*n-3*k+1,n-k)/k!.

%o (PARI) a(n) = n!*sum(k=0, n, (2*n-k+1)^(k-1)*binomial(5*n-3*k+1, n-k)/k!);

%Y Cf. A377745, A380753.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 01 2025