A362155 -id:A362155 - 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).

A372013 G.f. A(x) satisfies A(x) = 1/( 1 + x(1 - 9x*A(x))^(1/3) ).

Original entry on oeis.org

1, -1, 4, -1, 46, 149, 1351, 8441, 63499, 462752, 3514807, 26923478, 209566927, 1647633779, 13079663527, 104649229988, 843120766711, 6833665175513, 55683581174641, 455878084448132, 3748025535972448, 30931714278955736, 256150668109462507

Offset: 0

Seiichi Manyama, Apr 19 2024

sign

Cf. A166587, A362155, A372012.

a(n) = (-1)^n*sum(k=0, n, 9^(n-k)*binomial(n, k)*binomial(k/3, n-k)/(n-k+1));

a(n) = (-1)^n * Sum_{k=0..n} 9^(n-k) * binomial(n,k) * binomial(k/3,n-k)/(n-k+1).

cp's OEIS Frontend

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

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A372013 G.f. A(x) satisfies A(x) = 1/( 1 + x(1 - 9x*A(x))^(1/3) ).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A372013 G.f. A(x) satisfies A(x) = 1/( 1 + x*(1 - 9*x*A(x))^(1/3) ).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A372013 G.f. A(x) satisfies A(x) = 1/( 1 + x(1 - 9x*A(x))^(1/3) ).