# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a295517 Showing 1-1 of 1 %I A295517 #5 Dec 18 2017 04:15:49 %S A295517 1,2,-1,6,-5,-1,27,-31,-11,1,167,-252,-136,28,1,1310,-2491,-1864,656, %T A295517 94,-1,12394,-28603,-27583,13952,3718,-421,-1,137053,-372765,-440425, %U A295517 290431,113119,-24739,-2379,1,1733325,-5433312,-7596496,6162480,3142746,-1010144,-189768,16080,1 %N A295517 Triangle read by rows, T(n, k) the coefficients of some polynomials in Pi, for n >= 0 and 0 <= k <= n. %F A295517 Consider the polynomial p_n(x) with e.g.f. exp(-x)/(1 + log(-1-x)). After multiplying with -(Pi-1)^(n+1) and then substituting i by 1 this becomes a polynomial in Pi, the coefficients of which in ascending order constitute row n of the triangle. The constant coefficients are A291979. %e A295517 The first few polynomials are: %e A295517 1 %e A295517 2 - Pi %e A295517 6 - 5 Pi - Pi^2 %e A295517 27 - 31 Pi - 11 Pi^2 + Pi^3 %e A295517 167 - 252 Pi - 136 Pi^2 + 28 Pi^3 + Pi^4 %e A295517 1310 - 2491 Pi - 1864 Pi^2 + 656 Pi^3 + 94 Pi^4 - Pi^5 %e A295517 12394 - 28603 Pi - 27583 Pi^2 + 13952 Pi^3 + 3718 Pi^4 - 421 Pi^5 - Pi^6 %e A295517 The triangle starts: %e A295517 0: 1 %e A295517 1: 2, -1 %e A295517 2: 6, -5, -1 %e A295517 3: 27, -31, -11, 1 %e A295517 4: 167, -252, -136, 28, 1 %e A295517 5: 1310, -2491, -1864, 656, 94, -1 %e A295517 6: 12394, -28603, -27583, 13952, 3718, -421, -1 %e A295517 7: 137053, -372765, -440425, 290431, 113119, -24739, -2379, 1 %p A295517 A295517_poly := proc(n) assume(x<-1); exp(-x)/(1 + log(-1-x)): series(%, x, n+1): %p A295517 simplify(-(Pi-1)^(n+1)*n!*coeff(%, x, n)); subs(I=1, %) end: %p A295517 seq(seq(coeff(A295517_poly(n), Pi, k), k=0..n), n=0..8); %Y A295517 Cf. A291979. %K A295517 sign,tabl %O A295517 0,2 %A A295517 _Peter Luschny_, Dec 17 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE