A295517 Triangle read by rows, T(n, k) the coefficients of some polynomials in Pi, for n >= 0 and 0 <= k <= n.
1, 2, -1, 6, -5, -1, 27, -31, -11, 1, 167, -252, -136, 28, 1, 1310, -2491, -1864, 656, 94, -1, 12394, -28603, -27583, 13952, 3718, -421, -1, 137053, -372765, -440425, 290431, 113119, -24739, -2379, 1, 1733325, -5433312, -7596496, 6162480, 3142746, -1010144, -189768, 16080, 1
Offset: 0
Examples
The first few polynomials are:
1
2 - Pi
6 - 5 Pi - Pi^2
27 - 31 Pi - 11 Pi^2 + Pi^3
167 - 252 Pi - 136 Pi^2 + 28 Pi^3 + Pi^4
1310 - 2491 Pi - 1864 Pi^2 + 656 Pi^3 + 94 Pi^4 - Pi^5
12394 - 28603 Pi - 27583 Pi^2 + 13952 Pi^3 + 3718 Pi^4 - 421 Pi^5 - Pi^6
The triangle starts:
0: 1
1: 2, -1
2: 6, -5, -1
3: 27, -31, -11, 1
4: 167, -252, -136, 28, 1
5: 1310, -2491, -1864, 656, 94, -1
6: 12394, -28603, -27583, 13952, 3718, -421, -1
7: 137053, -372765, -440425, 290431, 113119, -24739, -2379, 1
Crossrefs
Cf. A291979.
Programs
Formula
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.