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.

A363423 G.f. satisfies A(x) = exp( Sum_{k>=1} A(3*x^k) * x^k/k ).

Original entry on oeis.org

1, 1, 4, 40, 1126, 92440, 22559276, 16468584194, 36033333480881, 236450784546518006, 4654297351684653345788, 274836259327539399144691019, 48686693681325683653963188907344, 25874153864215746591981599665978198380
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, 3*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))^(3^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(d-1) * a(d-1) ) * a(n-k).

A363427 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(4*x^k) * x^k/k ).

Original entry on oeis.org

1, 1, 4, 68, 4422, 1136646, 1165077220, 4773325045092, 78210934437541505, 5125710024629047469249, 1343679254641311248179226112, 1408951161809404147369817577873792, 5909570902737024213107077083032728540592
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, 4*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))^(4^k * a(k)).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d * 4^(d-1) * 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).
Showing 1-3 of 3 results.