A395385 a(n) = (2*n)! * [x^(2*n)] 1 / cos(x)^7.

1, 7, 161, 6727, 426881, 37611847, 4355312801, 638346159367, 115193184593921, 25053072226385287, 6455730412503886241, 1943529232047206865607, 675604198955894262885761, 268470392613462818311216327, 120904332733253591657292568481, 61240906503567861473174429293447

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = -(1/64) * Sum_{k=0..n-1} (-1)^(n-k) * (35 + 21*9^(n-k) + 7*25^(n-k) + 49^(n-k)) * binomial(2*n,2*k) * a(k).

a(n) = (1/720) * (225*A000364(n) + 259*A000364(n+1) + 35*A000364(n+2) + A000364(n+3)).

Prog

(PARI) a(n) = my(x='x+O('x^(2*n+1))); (2*n)!*polcoef(1/cos(x)^7, 2*n);

Crossrefs

Cf. A000364, A326327, A385343, A395390.

Sequence in context: A121786 A316947 A083153 * A320337 A214350 A208263

Adjacent sequences: A395382 A395383 A395384 * A395386 A395387 A395388

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2026

Status

approved