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 1-2 of 2 results.

A364430 G.f. satisfies A(x) = 1 - x*A(x)*(1 - 2*A(x)^3).

Original entry on oeis.org

1, 1, 7, 61, 603, 6443, 72517, 846995, 10170685, 124780525, 1557347467, 19710577873, 252386341335, 3263626001751, 42558647522697, 559032393114023, 7390085367865081, 98242108076244665, 1312529311579827631, 17613845480108029957, 237322279651518516019
Offset: 0

Views

Author

Seiichi Manyama, Jul 24 2023

Keywords

Crossrefs

Cf. A001003, A153232.
Cf. A364431, A364432, A364437.

Programs

  • Maple
    A364430 := proc(n)
    (-1)^n*add((-2)^k* binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1),k=0..n) ;
end proc:
seq(A364430(n),n=0..70); # R. J. Mathar, Jul 25 2023
  • PARI
    a(n) = (-1)^n*sum(k=0, n, (-2)^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));

Formula

a(n) = (-1)^n * Sum_{k=0..n} (-2)^k * binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1).
D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-566*n^3 +1335*n^2 -1105*n +312)*a(n-1) +3*(943*n^3 -5739*n^2 +11016*n -6748)*a(n-2) +18*(-250*n^3 +2499*n^2 -8233*n +8938)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) +81*(10*n -51)*(n-4) *(n-5)*a(n-5) +243*(n-5) *(n-6)*(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023

A364431 G.f. satisfies A(x) = 1 + x*A(x)*(1 + 2*A(x)^3).

Original entry on oeis.org

1, 3, 27, 351, 5319, 87885, 1535517, 27898101, 521740197, 9977087439, 194191054263, 3834392341779, 76619557946475, 1546479815079321, 31482877148802873, 645689728734541929, 13328555370318744777, 276704344407952939131, 5773556701375333682355
Offset: 0

Views

Author

Seiichi Manyama, Jul 24 2023

Keywords

Crossrefs

Cf. A103210, A348912.
Cf. A364430, A364432.

Programs

  • Maple
    A364431 := proc(n)
    add(2^k* binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1),k=0..n) ;
end proc:
seq(A364431(n),n=0..70); # R. J. Mathar, Jul 25 2023
  • PARI
    a(n) = sum(k=0, n, 2^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));

Formula

a(n) = Sum_{k=0..n} 2^k * binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1).
D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-458*n^3 +201*n^2 +401*n -216)*a(n-1) +3*(-1105*n^3 +6549*n^2 -11384*n +5796)*a(n-2) +18*(-262*n^3 +2877*n^2 -10295*n +12006)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) -81*(10*n-51) *(n-4)*(n-5)*a(n-5) +243*(n-5)*(n-6) *(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023
Showing 1-2 of 2 results.

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

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