This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355473 #15 Feb 21 2023 23:25:30 %S A355473 1,1,3,28,497,12736,517297,28793248,2095968065,199522773568, %T A355473 23839495688321,3482169003693304,616298415199306369, %U A355473 130134007837039167040,32272959284595295173377,9313050358489324003967176,3101245112865402456422252033 %N A355473 Expansion of Sum_{k>=0} x^k/(1 - k^3 * x)^(k+1). %H A355473 Winston de Greef, <a href="/A355473/b355473.txt">Table of n, a(n) for n = 0..235</a> %F A355473 E.g.f.: Sum_{k>=0} exp(k^3 * x) * x^k/k!. %F A355473 a(n) = Sum_{k=0..n} k^(3*(n-k)) * binomial(n,k). %o A355473 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k^3*x)^(k+1))) %o A355473 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp(k^3*x)*x^k/k!))) %o A355473 (PARI) a(n) = sum(k=0, n, k^(3*(n-k))*binomial(n, k)); %Y A355473 Cf. A000248, A135746, A355464. %K A355473 nonn %O A355473 0,3 %A A355473 _Seiichi Manyama_, Jul 03 2022