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 A276750 #15 Sep 17 2017 18:06:04
%S A276750 1,5,22,117,821,7796,101417,1810093,44561794,1515368605,71428667861,
%T A276750 4677209119632,426268582440013,54220470799325101,9632796180856419722,
%U A276750 2397253932245127919389,835827069207839232602401,409329501365419311969616628,281600921299273941316256813501,272632759803890415543364253988037,371636574592049013061911521355729422,713832787857018847209335427225631327093
%N A276750 L.g.f.: Sum_{n>=1} [ Sum_{k>=1} k^n * x^k ]^n / n.
%C A276750 L.g.f. equals the logarithm of the g.f. of A156170.
%H A276750 Paul D. Hanna, <a href="/A276750/b276750.txt">Table of n, a(n) for n = 1..150</a>
%F A276750 L.g.f.: Sum_{n>=1} [ Sum_{k=1..n} A008292(n,k) * x^k / (1-x)^(n+1) ]^n / n, where A008292 are the Eulerian numbers.
%e A276750 L.g.f.: A(x) = x + 5*x^2/2 + 22*x^3/3 + 117*x^4/4 + 821*x^5/5 + 7796*x^6/6 + 1810093*x^7/7 + 44561794*x^8/8 + 1515368605*x^9/9 + 71428667861*x^10/10 +...
%e A276750 such that A(x) equals the series:
%e A276750 A(x) = Sum_{n>=1} (x + 2^n*x^2 + 3^n*x^3 +...+ k^n*x^k +...)^n/n.
%e A276750 This logarithmic series can be written using the Eulerian numbers like so:
%e A276750 A(x) = x/(1-x)^2 + (x + x^2)^2/(1-x)^6/2 + (x + 4*x^2 + x^3)^3/(1-x)^12/3 + (x + 11*x^2 + 11*x^3 + x^4)^4/(1-x)^20/4 + (x + 26*x^2 + 66*x^3 + 26*x^4 + x^5)^5/(1-x)^30/5 + (x + 57*x^2 + 302*x^3 + 302*x^4 + 57*x^5 + x^6)^6/(1-x)^42/6 +...+ [ Sum_{k=1..n} A008292(n,k) * x^k ]^n / (1-x)^(n*(n+1))/n +...
%e A276750 where
%e A276750 exp(A(x)) = 1 + x + 3*x^2 + 10*x^3 + 41*x^4 + 219*x^5 + 1602*x^6 + 16635*x^7 + 247171*x^8 + 5242108*x^9 + 157390565*x^10 +...+ A156170(n)*x^n +...
%o A276750 (PARI) {a(n) = n * polcoeff( sum(m=1, n, sum(k=1, n, k^m*x^k +x*O(x^n))^m/m ), n)}
%o A276750 for(n=1, 20, print1(a(n), ", "))
%o A276750 (PARI) {A008292(n, k) = sum(j=0, k, (-1)^j * (k-j)^n * binomial(n+1, j))}
%o A276750 {a(n) = my(A=1, Oxn=x*O(x^n)); A = sum(m=1, n+1, sum(k=1, m, A008292(m, k)*x^k/(1-x +Oxn)^(m+1) )^m / m ); n*polcoeff(A, n)}
%o A276750 for(n=1, 20, print1(a(n), ", "))
%Y A276750 Cf. A156170, A276753, A276754, A276906, A008292, A292502.
%K A276750 nonn
%O A276750 1,2
%A A276750 _Paul D. Hanna_, Sep 17 2016