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.

Previous Showing 11-12 of 12 results.

A364333 G.f. satisfies A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^6).

Original entry on oeis.org

1, 2, 17, 216, 3224, 52640, 910452, 16392140, 303996224, 5767278431, 111401778266, 2183535060362, 43319505976084, 868220464851417, 17552981176788200, 357544690982030744, 7330803752675100908, 151172599088871911072, 3133367418601958989295, 65242183918761533467216
Offset: 0

Views

Author

Seiichi Manyama, Jul 18 2023

Keywords

Crossrefs

Cf. A007863, A069271, A073157, A215654, A215715, A364331.
Cf. A239109, A364339, A364340.
Cf. A200718.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(2*n+4*k+1, k)*binomial(2*n+4*k+1, n-k)/(2*n+4*k+1));

Formula

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

A379021 Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^2 ).

Original entry on oeis.org

1, 4, 26, 206, 1813, 17032, 167287, 1697044, 17643322, 186997570, 2012973499, 21948003052, 241883091289, 2690117648372, 30153678822007, 340305271736134, 3863616751855069, 44097785533620550, 505692279260755753, 5823592506326814874, 67320958983831426221
Offset: 0

Views

Author

Seiichi Manyama, Dec 14 2024

Keywords

Links

Crossrefs

Cf. A007863, A379023, A379024.
Cf. A215654, A379022.

Programs

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

Formula

G.f. A(x) satisfies:
(1) A(x) = exp( Sum_{k>=1} A379022(k) * x^k/k ).
(2) A(x) = ( (1 + x*A(x)) * (1 + x*A(x)^(3/2)) )^2.
(3) A(x) = B(x)^2 where B(x) is the g.f. of A215654.
a(n) = (1/(n+1)) * [x^n] ( (1 + x)/(1 - x - x^2) )^(2*(n+1)).
a(n) = 2 * Sum_{k=0..n} binomial(2*n+k+2,k) * binomial(2*n+k+2,n-k)/(2*n+k+2) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(2*n+k+2,n-k).
Previous Showing 11-12 of 12 results.

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

Content is available under The OEIS End-User License Agreement.