A380210 - OEIS

%I #11 Jan 17 2025 09:05:54

%S 1,5,40,365,3835,44420,559375,7569875,108989500,1659791375,

%T 26571465625,445392932000,7785570546625,141513486039125,

%U 2666916967144000,52000124771091125,1046623556362721875,21712732294602537500,463350533965622059375,10162009318486049571875

%N Expansion of e.g.f. exp( (1+2*x)^(5/2) - 1 ).

%C a(36) is negative.

%F a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * Stirling1(n,k) * Bell(k).

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+2*x)^(5/2)-1)))

%Y Cf. A380209.

%K changed,sign

%O 0,2

%A _Seiichi Manyama_, Jan 16 2025