A395382 a(n) = (2*n)! * [x^(2*n)] 1 / cos(x)^4.

1, 4, 56, 1504, 64256, 3963904, 332205056, 36246728704, 4988057747456, 844642265595904, 172538313119891456, 41830529289372565504, 11873214587450798637056, 3900031765704228946837504, 1467739915646067947922784256, 627377259124838374713698811904

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = -(1/8) * Sum_{k=0..n-1} (-1)^(n-k) * (4^(n-k+1) + 16^(n-k)) * binomial(2*n,2*k) * a(k).

a(n) = (1/6) * (4*A000182(n+1) + A000182(n+2)).

Prog

(PARI) a(n) = my(x='x+O('x^(2*n+1))); (2*n)!*polcoef(1/cos(x)^4, 2*n);

Crossrefs

Cf. A000182, A326327, A385343, A395387.

Sequence in context: A377428 A377429 A277038 * A009536 A009558 A113583

Adjacent sequences: A395379 A395380 A395381 * A395383 A395384 A395385

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2026

Status

approved