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.

A371538 G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^3.

Original entry on oeis.org

1, 3, 18, 151, 1440, 14835, 160793, 1806849, 20859129, 245905348, 2947869600, 35825319390, 440372147956, 5465555197818, 68396554601013, 862066323857486, 10933638171672105, 139439595024315675, 1787056241039876890, 23003636498360053905, 297283046361025602900
Offset: 0

Views

Author

Seiichi Manyama, Mar 26 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 3*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+3, k)/(6*k+3));

Formula

a(n) = 3 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+3,k)/(6*k+3).
G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A349362.

A371537 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1+x))^2.

Original entry on oeis.org

1, 2, 11, 90, 845, 8620, 92792, 1037474, 11930952, 140223730, 1676824810, 20336742860, 249554057158, 3092735367966, 38653949888993, 486656046354650, 6166315484899445, 78573243500307870, 1006223574171080479, 12943581721362983708, 167170200918998754129
Offset: 0

Views

Author

Seiichi Manyama, Mar 26 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+2, k)/(6*k+2));

Formula

a(n) = 2 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+2,k)/(6*k+2).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349362.

A371539 G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/2) / (1+x))^4.

Original entry on oeis.org

1, 4, 26, 224, 2171, 22600, 246754, 2787856, 32318849, 382266056, 4594893684, 55966343520, 689245218880, 8568130064280, 107371481352870, 1354944741505580, 17203182641794020, 219604431213873060, 2816826935574781930, 36286757255072528360, 469266638574298431490
Offset: 0

Views

Author

Seiichi Manyama, Mar 26 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 4*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+4, k)/(6*k+4));

Formula

a(n) = 4 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+4,k)/(6*k+4).
G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A349362.

A371541 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^6.

Original entry on oeis.org

1, 6, 45, 410, 4110, 43746, 485237, 5547396, 64901670, 773296320, 9350929395, 114464359296, 1415620823147, 17661466502796, 222017667461685, 2809362871991380, 35755481454362355, 457410181217186886, 5878378983480722222, 75856853080508789406
Offset: 0

Views

Author

Seiichi Manyama, Mar 26 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+6, k)/(k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+6,k)/(k+1).
G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A349362.
Showing 1-4 of 4 results.