cp's OEIS Frontend

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.

A291449 Numerators of Integral_{x=0..1} P(n, x)^3 with P(n, x) = Sum_{k=0..n} (-1)^(n-k)* Stirling2(n, k)*k!*x^k.

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%I A291449 #11 Jun 15 2019 10:31:33
%S A291449 1,1,13,1,43,-61,728877,81739,-1779449713,-2112052153,730622680308569,
%T A291449 113221320488699,-3660430816956396309,-3021604582205161,
%U A291449 21842539561810574341396283,66747470298418575790593659,-124586733960451680357554181608419,-28471605423890788373026535240299
%N A291449 Numerators of Integral_{x=0..1} P(n, x)^3 with P(n, x) = Sum_{k=0..n} (-1)^(n-k)* Stirling2(n, k)*k!*x^k.
%C A291449 Consider a family of integrals I(m, n) = Integral_{x=0..1} P(n, x)^m with P(n, x) = Sum_{k=0..n} (-1)^(n-k)*Stirling2(n, k)*k!*x^k. I(1, n) are the Bernoulli numbers A164555/A027642, I(2, n) are the Bernoulli median numbers A212196/A181131, I(3, n) are the numbers A291449/A291450. The coefficients of the polynomials P(n, x)^m are for m = 1 A290694/A290695, for m = 2 A291447/A291448. (See A290694 for further comments.)
%p A291449 # Function BG_row is defined in A290694.
%p A291449 seq(BG_row(3, n, "num", "val"), n=0..17);
%t A291449 P[n_, x_] := Sum[(-1)^(n-k)*StirlingS2[n, k]*k!*x^k, {k, 0, n}];
%t A291449 a[n_] := Integrate[P[n, x]^3, {x, 0, 1}] // Numerator;
%t A291449 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Jun 15 2019 *)
%Y A291449 Cf. A164555/A027642, A212196/A181131, A291449/A291450, A290694/A290695, A291447/A291448.
%K A291449 sign,frac
%O A291449 0,3
%A A291449 _Peter Luschny_, Aug 24 2017