A361792 Expansion of 1/sqrt(1 - 4*x/(1+x)^6).

1, 2, -6, -10, 66, 60, -750, -236, 8682, -2098, -100792, 80286, 1162458, -1603412, -13225764, 26767020, 147428498, -409582818, -1596563202, 5941802122, 16587101544, -83014131140, -161717252990, 1126247965980, 1411774064970, -14905602076350

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n+5*k-1,n-k).

n*a(n) = -( (3*n-5)*a(n-1) + (17*n-24)*a(n-2) + 35*(n-3)*a(n-3) + 35*(n-4)*a(n-4) + 21*(n-5)*a(n-5) + 7*(n-6)*a(n-6) + (n-7)*a(n-7) ) for n > 6.

a(0) = 1; a(n) = (2/n) * Sum_{k=0..n-1} (-1)^(n-1-k) * (n+k) * binomial(n+4-k,5) * a(k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1+x)^6))

Crossrefs

Cf. A006139, A137635, A360133, A361790, A361791.

Cf. A360132.

Sequence in context: A095107 A115113 A163788 * A324547 A093880 A080397

Adjacent sequences: A361789 A361790 A361791 * A361793 A361794 A361795

Keyword

sign

Author

Seiichi Manyama, Mar 24 2023

Status

approved