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.

A379328 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^3) * (1 + 2*x*A(x)) ).

Original entry on oeis.org

1, 2, 8, 44, 272, 1808, 12616, 91136, 675712, 5112576, 39316480, 306402304, 2414543328, 19207303168, 154030314752, 1243912552448, 10107398806016, 82573989969920, 677862373390592, 5588755066388480, 46257005500080128, 384210240316375040, 3201482490107076608
Offset: 0

Views

Author

Seiichi Manyama, Dec 21 2024

Keywords

Crossrefs

Cf. A379326, A379327.
Cf. A198953, A379280.

Programs

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

A379382 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x))/(1 - 2*x*A(x)^2) ).

Original entry on oeis.org

1, 2, 8, 48, 336, 2560, 20608, 172416, 1484288, 13062144, 116977664, 1062600704, 9767067648, 90673700864, 848971661312, 8007542571008, 76014137180160, 725681289822208, 6962697126019072, 67105309925048320, 649362348326256640, 6306663216709632000
Offset: 0

Views

Author

Seiichi Manyama, Dec 22 2024

Keywords

Crossrefs

Cf. A138020, A379383.
Cf. A151374, A379327, A379330.
Cf. A106228.

Programs

  • PARI
    a(n) = 2^n*sum(k=0, n, binomial(n/2+3*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+3*k/2-1/2,k) * binomial(n/2+k/2+1/2,n-k)/(n+k+1).
a(n) = 2^n * A106228(n).
Showing 1-3 of 3 results.

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

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