A292072 Main diagonal of A292068.
1, -1, -3, -20, 66, 4439, 454420, 4873175, -3803048954, -7320203267692, -1403057989033446, 6669491545211096686, 78492109668913945526447, 69591502229308312804788424, -6243846072108996200105800383026, -604234376454072219680822138902122079
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..79
Programs
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Maple
b:= proc(n, i, k) option remember; (m-> `if`(m -
Mathematica
b[n_, i_, k_] := b[n, i, k] = Function[m, If[m < n, 0, If[n == m, i!^k, b[n, i - 1, k] + If[i > n, 0, i^k*b[n - i, i - 1, k]]]]][i*(i + 1)/2]; g[n_, k_] := g[n, k] = If[n == 0, 1, -Sum[b[n-i, n-i, k]*g[i, k], {i, 0, n-1}]]; a[n_] := g[n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jun 03 2018, after Alois P. Heinz *) -
PARI
{a(n) = polcoeff(1/prod(k=1, n, 1+k^n*x^k+x*O(x^n)), n)} -
Python
from sympy.core.cache import cacheit from sympy import factorial as f @cacheit def b(n, i, k): m=i*(i + 1)/2 return 0 if mn else i**k*b(n - i, i - 1, k)) @cacheit def g(n, k): return 1 if n==0 else -sum([b(n - i, n - i, k)*g(i, k) for i in range(n)]) def a(n): return g(n, n) print([a(n) for n in range(16)]) # Indranil Ghosh, Sep 14 2017, after Maple program
Formula
a(n) = [x^n] Product_{k=1..n} 1/(1 + k^n*x^k).