A373658
a(n) = Sum_{k=0..n} binomial(n, k)*A050446(n, n - k). Alternating row sums of A373660.
Original entry on oeis.org
1, 3, 13, 88, 749, 8128, 105453, 1606368, 28047561, 552980736, 12149820237, 294451219712, 7803392603109, 224513730740224, 6969658947747357, 232210548740331008, 8265038127738534417, 312994090288528379904, 12565925964816171109069, 533124629548518534705152
Offset: 0
-
a := n -> local k; add(binomial(n, k) * A050446(n, n - k), k = 0..n):
seq(a(n), n = 0..19);
Original entry on oeis.org
1, 2, 6, 30, 190, 1547, 15106, 173502, 2286648, 34053437, 565424068, 10358963615, 207582616995, 4516836844067, 106059101583274, 2673073911292478, 71978776046880670, 2062324447652722085, 62647209605811093549, 2011144064488835839006, 68034719732835699646658
Offset: 0
-
from functools import cache
@cache
def T(n, k):
return T(n, k - 1) + sum(T(2 * j, k - 1) * T(n - 1 - 2 * j, k)
for j in range(1 + (n - 1) // 2)) if k > 0 else 1
def a(n): return T(n, n)
print([a(n) for n in range(21)])
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