cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A379327 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^2) * (1 + 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 6, 22, 88, 372, 1634, 7382, 34078, 160034, 762078, 3671178, 17858476, 87599696, 432804190, 2151867226, 10758455224, 54053627604, 272780539742, 1382047628514, 7027307040920, 35848334763884, 183417043984246, 941007480667474, 4839875674661214, 24950493967407850
Offset: 0

Views

Author

Seiichi Manyama, Dec 21 2024

Keywords

Crossrefs

Cf. A379326, A379328.
Cf. A007863, A379279.

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2+k/2+1/2, k)*binomial(n/2+k/2+1/2, n-k)/(n+k+1));

Formula

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

A379326 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x) * (1 + 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 2, 2, 0, 0, -2, 2, -2, 6, -10, 14, -28, 52, -86, 158, -296, 528, -966, 1806, -3328, 6160, -11542, 21590, -40418, 76118, -143598, 271138, -513524, 974620, -1851962, 3525682, -6723794, 12839190, -24550602, 47010286, -90122848, 172970032, -332352998, 639260230
Offset: 0

Views

Author

Seiichi Manyama, Dec 21 2024

Keywords

Crossrefs

Cf. A379327, A379328.

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2-k/2+1/2, k)*binomial(n/2-k/2+1/2, n-k)/(n-k+1));

Formula

G.f.: -(1+2*x) / (x*(1+2*x) - sqrt((x*(1+2*x))^2 + (1+2*x))).
a(n) = 2^n * Sum_{k=0..n} binomial(n/2-k/2+1/2,k) * binomial(n/2-k/2+1/2,n-k)/(n-k+1).

A379383 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^3) ).

Original entry on oeis.org

1, 2, 10, 80, 750, 7680, 83252, 939008, 10905942, 129548288, 1566565452, 19220267008, 238662840780, 2993651974144, 37876206019560, 482802294325248, 6194365014836582, 79930063134392320, 1036640587694252380, 13505632613590630400, 176673045664669396132, 2319654465118014537728
Offset: 0

Views

Author

Seiichi Manyama, Dec 22 2024

Keywords

Crossrefs

Cf. A138020, A379382.
Cf. A078531, A379328, A379331.

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2+2*k-1/2, k)*binomial(n/2+k+1/2, n-k)/(n+2*k+1));

Formula

a(n) = 2^n * Sum_{k=0..n} binomial(n/2+2*k-1/2,k) * binomial(n/2+k+1/2,n-k)/(n+2*k+1).
a(n) = 2^n * Sum_{k=0..n} binomial(n,k) * binomial(n/2+2*k+1/2,n)/(n+4*k+1).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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