A355464 - OEIS

%I #15 Jul 03 2022 09:34:57

%S 1,2,4,17,210,9217,1399298,811229225,2071392232962,20710319937493889,

%T 1137259214532706572162,255141201504146525745627265,

%U 348787971214016591166179037803522,2262996819897931095524655885144485185409

%N Expansion of Sum_{k>=0} x^k/(1 - k^k * x)^(k+1).

%F E.g.f.: Sum_{k>=0} exp(k^k * x) * x^k/k!.

%F a(n) = Sum_{k=0..n} k^(k*(n-k)) * binomial(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^k*x)^(k+1)))

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, exp(k^k*x)*x^k/k!)))

%o (PARI) a(n) = sum(k=0, n, k^(k*(n-k))*binomial(n, k));

%Y Cf. A086331, A320287, A349893, A355440, A355463.

%Y Cf. A000248, A135746, A355473.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 03 2022