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.

A171208 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^7.

Original entry on oeis.org

1, 1, 14, 476, 31640, 3953488, 939383200, 433281169216, 393718899904640, 710399428248892928, 2554705943898166145024, 18342976469146094416494592, 263185684727811758287894478848, 7549222852919288301041224694890496, 432993292623369448352459156263293419520
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]^7 + 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)^7); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} Product_{k=1..7} a(x_k). - Seiichi Manyama, Jul 08 2025

A171195 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^5).

Original entry on oeis.org

1, 1, 11, 281, 13731, 1245601, 213268203, 70580511385, 45914883339027, 59241954299963729, 152258885235304955131, 781096727709105092232777, 8006263111571482684378716067, 164048440920655457493139473502081
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^5) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^5) ); polcoeff(A, n)}

Formula

a(n) ~ c * 2^(n*(n-1)/2) * 5^n, where c = 0.444871440417987089861554304425221691031547... - Vaclav Kotesovec, Nov 03 2021
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} (1/2)^x_1 * Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 06 2025

A171197 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^7).

Original entry on oeis.org

1, 1, 15, 533, 36415, 4624621, 1108685495, 513716588981, 467874135168079, 845152554936920445, 3041003426951554000167, 21840734269889733272106629, 313415404907854466274076819391, 8990640466019774671530066108827853
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^7) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^7) ); polcoeff(A, n)}

Formula

a(n) ~ c * 2^(n*(n-1)/2) * 7^n, where c = 0.307176924551399606223470587229647816147018... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_8>=0 and x_1+x_2+...+x_8=n-1} (1/2)^x_1 * Product_{k=1..8} a(x_k). - Seiichi Manyama, Jul 06 2025
Showing 1-3 of 3 results.