A257372 a(n) = denominators of A255935(n) * triangle T(n,k) for Bernoulli(k+2), k=0 to n-1.

1, 6, 6, 15, 30, 21, 42, 15, 30, 33, 66, 1365, 2730, 3, 6, 255, 510, 399, 798, 165, 330, 69, 138, 1365, 2730, 3, 6, 435, 870, 7161, 14322, 255, 510, 3, 6, 959595, 1919190, 3, 6, 6765, 13530, 903, 1806, 345, 690

Offset: 0

Author

Paul Curtz, Apr 21 2015

Keywords

• nonn

Comments

Generally, A255935(n) multiplied by triangle T(n,k) for s(k), k=0 to n-1 yields an autosequence of the first kind (a sequence whose main diagonal is 0's).

Here s(k) = 1/6, 0, -1/30, ... from A164555(n+2)/A027642(n+2). Hence

0 = 0/1

1/6, 0 = 1/6

1/6, 0, 0 = 1/6

1/6, 0, -1/10, 0 = 1/15

1/6, 0, -1/5, 0, 0 =-1/30

... .

a(n) are the row sums denominators.

Compare to A051716(n+2)/A051717(n+2).

Hence the difference table

0, 1/6, 1/6, 1/15, -1/30, -1/21, 1/42, ...

1/6, 0, -1/10, -1/10, -1/70, 1/14, ...

-1/6, -1/10, 0, 3/35, 3/35, ...

1/15, 1/10, 3/35, 0, ...

1/30, -1/70, -3/35, ...

-1/21, -1/14, ...

-1/42, ...

... .

Crossrefs

Cf. A255935, A027641/A027642, A164555/A027642, A001897, A002445, A040000, A051716/A051717.

Formula

a(2n) = A002445(n).

a(2n+3) = A001897(n+2).

a(2n+2) = A040000(n) * a(2n+1).