A362156 -id:A362156 - cp's OEIS frontend

A362154 Expansion of 1/(1 + x * sqrt(1-4*x)).

1, -1, 3, -3, 11, -5, 51, 35, 335, 689, 3055, 9073, 33891, 114425, 413623, 1464661, 5304803, 19199859, 70161499, 257270227, 948639463, 3511150611, 13047799395, 48649126799, 181968324231, 682577156519, 2567180111683, 9678596662499, 36571577629911

Offset: 0

Seiichi Manyama, Apr 09 2023

Cf. A039834, A362155.

Cf. A000984, A362156, A362161.

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

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

A362157 Expansion of -1/(1 - x * (1-9*x)^(1/3)).

Original entry on oeis.org

-1, -1, 2, 14, 62, 317, 1967, 13544, 98012, 731273, 5581682, 43377617, 342035204, 2729286017, 21996002729, 178769985791, 1463465010995, 12055667829734, 99858109234379, 831150925169516, 6947819513136614, 58303331305857293, 490961900646977570

Offset: 0

Seiichi Manyama, Apr 09 2023

Cf. A004987, A362156.

my(N=30, x='x+O('x^N)); Vec(-1/(1-x*(1-9*x)^(1/3)))

a(n) = -Sum_{k=0..n} (-9)^k * binomial((n-k)/3,k).

A362158 Expansion of e.g.f. -exp(x * sqrt(1-4*x)).

Original entry on oeis.org

-1, -1, 3, 23, 119, 1119, 19259, 417143, 10567983, 309715199, 10335277619, 386840046999, 16045111426343, 730346987476703, 36191354975508459, 1939288175212058999, 111724538084900577119, 6886112439566787983103, 452112545350650426838883

Offset: 0

Seiichi Manyama, Apr 10 2023

Cf. A362156.

my(N=20, x='x+O('x^N)); Vec(serlaplace(-exp(x*sqrt(1-4*x))))

a(n) = - n! * Sum_{k=0..n} (-4)^k * binomial((n-k)/2,k)/(n-k)!.

a(n) ~ 2^(2*n - 5/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Apr 10 2023

cp's OEIS Frontend

A362154 Expansion of 1/(1 + x * sqrt(1-4*x)).

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A362157 Expansion of -1/(1 - x * (1-9*x)^(1/3)).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A362158 Expansion of e.g.f. -exp(x * sqrt(1-4*x)).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula