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.

A132228 a(n) = Sum_{k=0..n} C(n-1,k)^2*a(k)*a(n-k-1) for n>0 with a(0)=1.

Original entry on oeis.org

1, 1, 2, 8, 52, 504, 6808, 122304, 2820048, 81183200, 2853990496, 120321094656, 5991955466560, 347996920977664, 23312947041336960, 1784445116557881344, 154767015393810489600, 15098457734490931766784
Offset: 0

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Author

Paul D. Hanna, Aug 15 2007

Keywords

Comments

Let A(x) = Sum_{n>=0} a(n) * x^n / n!^2. Then A(x)^2 = A'(x) + x * A''(x). - Michael Somos, May 20 2018

Crossrefs

Cf. A001059.

Programs

  • PARI
    a(n)=if(n==0,1,sum(k=0,n-1,a(k)*a(n-k-1)*binomial(n-1,k)^2 ))
  • PARI
    {a(n) = my(A); if( n<0, 0, A = 1 + O(x); for( k=0, n, A = 1 + intformal( intformal(A^2) / x)); n!^2 * polcoeff(A,n))}; /* Michael Somos, May 20 2018 */

A346187 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^3 * a(k) * a(n-k-1).

Original entry on oeis.org

1, 1, 9, 279, 20655, 2997405, 753171615, 300907367775, 179603100388215, 152724638158940925, 178223093773584811875, 276909379421415142992975, 558708999223935430219474125, 1433526175506213101913925750425, 4594607165137022427482460137390625, 18114938314838093950739712451059177375
Offset: 0

Views

Author

Ilya Gutkovskiy, Jul 09 2021

Keywords

Crossrefs

Cf. A001059, A001147, A181543, A336195, A346186.

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^3 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}]
Showing 1-2 of 2 results.

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