A362586
Triangle read by rows, T(n, k) = A094088(n) * binomial(n, k).
Original entry on oeis.org
1, 1, 1, 7, 14, 7, 121, 363, 363, 121, 3907, 15628, 23442, 15628, 3907, 202741, 1013705, 2027410, 2027410, 1013705, 202741, 15430207, 92581242, 231453105, 308604140, 231453105, 92581242, 15430207, 1619195761, 11334370327, 34003110981, 56671851635, 56671851635, 34003110981, 11334370327, 1619195761
Offset: 0
[0] 1;
[1] 1, 1;
[2] 7, 14, 7;
[3] 121, 363, 363, 121;
[4] 3907, 15628, 23442, 15628, 3907;
[5] 202741, 1013705, 2027410, 2027410, 1013705, 202741;
A362585
Triangle read by rows, T(n, k) = A000670(n) * binomial(n, k).
Original entry on oeis.org
1, 1, 1, 3, 6, 3, 13, 39, 39, 13, 75, 300, 450, 300, 75, 541, 2705, 5410, 5410, 2705, 541, 4683, 28098, 70245, 93660, 70245, 28098, 4683, 47293, 331051, 993153, 1655255, 1655255, 993153, 331051, 47293, 545835, 4366680, 15283380, 30566760, 38208450, 30566760, 15283380, 4366680, 545835
Offset: 0
[0] 1;
[1] 1, 1;
[2] 3, 6, 3;
[3] 13, 39, 39, 13;
[4] 75, 300, 450, 300, 75;
[5] 541, 2705, 5410, 5410, 2705, 541;
[6] 4683, 28098, 70245, 93660, 70245, 28098, 4683;
-
def TransOrdPart(m, n) -> list[int]:
@cached_function
def P(m: int, n: int):
R = PolynomialRing(ZZ, "x")
if n == 0: return R(1)
return R(sum(binomial(m * n, m * k) * P(m, n - k) * x
for k in range(1, n + 1)))
T = P(m, n)
def C(k) -> int:
return sum(T[j] * binomial(n, k) for j in range(n + 1))
return [C(k) for k in range(n+1)]
def A362585(n) -> list[int]: return TransOrdPart(1, n)
for n in range(6): print(A362585(n))
Showing 1-2 of 2 results.