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.

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

A364432 G.f. satisfies A(x) = 1 + x*A(x)*(2 + A(x)^3).

Original entry on oeis.org

1, 3, 18, 162, 1728, 20169, 249318, 3207600, 42500700, 576012060, 7947785448, 111269613006, 1576658688480, 22568473199358, 325855352769588, 4740157737123696, 69405108247439676, 1022070746845708740, 15127922880893671704, 224931239520535651464
Offset: 0

Views

Author

Seiichi Manyama, Jul 24 2023

Keywords

Crossrefs

Cf. A047891, A348793.
Cf. A364430, A364431.

Programs

  • Maple
    A364432 := proc(n)
    add(2^(n-k)* binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1),k=0..n) ;
end proc:
seq(A364432(n),n=0..70); # R. J. Mathar, Jul 25 2023
  • PARI
    a(n) = sum(k=0, n, 2^(n-k)*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));

Formula

a(n) = Sum_{k=0..n} 2^(n-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) +2*(-74*n^3 -375*n^2+ 665*n -252)*a(n-1) +12*(-337*n^3 +1941*n^2 -2984*n +1092)*a(n-2) +144*(-70*n^3 +861*n^2 -3347*n +4152)*a(n-3) +432*(n-4)*(31*n^2 -314*n +735)*a(n-4) -2592*(10*n-51) *(n-4)*(n-5)*a(n-5) +15552*(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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