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 1-4 of 4 results.

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).

A363440 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (4*x)^k/k ).

Original entry on oeis.org

1, 4, 32, 256, 2208, 19712, 183808, 1763328, 17332992, 173621248, 1766188288, 18196260864, 189474570240, 1990887063552, 21082432966656, 224766598100992, 2410570956881920, 25988893875994624, 281505478557407232, 3062014088362049536
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)*(4*x)^k/k)+x*O(x^n))); Vec(A);

Formula

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

A363441 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ).

Original entry on oeis.org

1, 2, 4, 16, 52, 208, 840, 3520, 15008, 65344, 288408, 1288416, 5813744, 26460800, 121333200, 559991712, 2599385536, 12127405952, 56837861376, 267473333120, 1263354463056, 5987210061184, 28461008374480, 135672151034304, 648406644570048
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, (-1)^(k+1)*subst(A, x, x^k)*(2*x)^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+2*x^(k+1))^a(k).
a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-2)^(k/d) * a(d-1) ) * a(n-k).

A363481 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(2*x^k) * x^k/k ).

Original entry on oeis.org

1, 2, 11, 108, 1969, 67542, 4473663, 582167944, 150236569819, 77226088637142, 79235069050108841, 162432444097491547308, 665648716390456030366881, 5454326724964994060395500598, 89374602386639273949112262243227
Offset: 0

Views

Author

Seiichi Manyama, Jun 04 2023

Keywords

Crossrefs

Programs

  • PARI
    seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, subst(A, x, 2*x^k)*x^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = B(x)^2 where B(x) is the g.f. of A363480.
A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(2^(k+1) * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 2^d * a(d-1) ) * a(n-k).
Showing 1-4 of 4 results.