Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of shift_x_plus_one of Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
- Premises
- shift_x_plus_one of Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- shift_x_plus_one of Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-cd198aa968243143· JSON- Operation
- Image under a basis map u^k -> P_k
{ "map": "A007318", "operation": "basis_map" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
basis_map, SHA-2560359ca3b2d75a2ee7d876ec45c953d5ce79391cb710b5c5ba7a85bc43e686668, 12,559 bytes (2,204 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-ff2ca64442a7da44(one_signed_coefficients)n-ff2ca64442a7da44(hadamard_kernel)n-ff2ca64442a7da44(real_rooted)