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.

A171204 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^5.

Original entry on oeis.org

1, 1, 10, 240, 11280, 1000080, 169100832, 55605632640, 36058105605120, 46450803286978560, 119290436529298554880, 611727201854914747760640, 6268994998754867059071385600, 128439243721180540266999017635840, 5261899692949082390205726962630000640, 431096933496167311430326245852780460769280
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1 + x*A[2x]^5 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^5); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l, m>=0 and i+j+k+l+m=n-1} a(i) * a(j) * a(k) * a(l) * a(m). - Seiichi Manyama, Jul 08 2025

A171206 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^6.

Original entry on oeis.org

1, 1, 12, 348, 19744, 2108784, 428817600, 169398274624, 131889504749568, 203937600707475456, 628561895904796999680, 3868208404121906515820544, 47571342639450113377565933568, 1169589733863427138021074362433536, 57499379103783344787572704263568097280, 5652994168279651703590653986228287051923456
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1+x*A[2x]^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^6); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 08 2025

A171207 G.f. satisfies: A(x) = (1 + x*A(2x))^6.

Original entry on oeis.org

1, 6, 87, 2468, 131799, 13400550, 2646848041, 1030386755856, 796631252763576, 1227659952939056640, 3777547269650299331856, 23228194648169000672639616, 285544368619000766118426358016, 7018967175754802830514246125923840, 345031382341287335424234252089128848384
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    terms = 15; A[] = 0; Do[A[x] = (1+x*A[2x])^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^6); polcoeff(A, n)}

Formula

Self-convolution 6th power of A171206 where a(n) = A171206(n+1)/2^n for n>=0.

Extensions

a(14) from Stefano Spezia, Apr 02 2025
Showing 1-3 of 3 results.