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.

A363424 G.f. satisfies A(x) = exp( Sum_{k>=1} A(4*x^k) * x^k/k ).

Original entry on oeis.org

1, 1, 5, 85, 5535, 1422815, 1458410395, 5975113492155, 97902240525033630, 6416219161308006188750, 1681979772433159156954845846, 1763685303864317080584539713676102, 7397434088431352859937186709876628421294
Offset: 0

Views

Author

Seiichi Manyama, Jun 01 2023

Keywords

Crossrefs

Programs

  • PARI
    seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, 4*x^k)*x^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(4^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 4^(d-1) * a(d-1) ) * a(n-k).

A363426 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(3*x^k) * x^k/k ).

Original entry on oeis.org

1, 1, 3, 30, 840, 68934, 16821865, 12280119400, 26868936914550, 176313989066991255, 3470564614854890465955, 204936840860491674903711726, 36304151491699938200267389259775, 19293550877461959142221066537253871070
Offset: 0

Views

Author

Seiichi Manyama, Jun 01 2023

Keywords

Crossrefs

Programs

  • PARI
    seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, 3*x^k)*x^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(k+1))^(3^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d * 3^(d-1) * a(d-1) ) * a(n-k).

A363439 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).

Original entry on oeis.org

1, 3, 18, 108, 702, 4698, 32913, 236844, 1747170, 13131639, 100239444, 774932832, 6055105590, 47742847875, 379381851684, 3035174325246, 24426965179593, 197622494260479, 1606332527049645, 13111628672610153, 107428845309125157
Offset: 0

Views

Author

Seiichi Manyama, Jun 02 2023

Keywords

Crossrefs

Programs

  • PARI
    seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*(3*x)^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-3*x^(k+1))^a(k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(k/d) * a(d-1) ) * a(n-k).
Showing 1-3 of 3 results.