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.

A371229 E.g.f. satisfies A(x) = 1 - x*A(x)^2*log(1 - x*A(x)^2).

Original entry on oeis.org

1, 0, 2, 3, 104, 630, 19944, 259560, 8718464, 185086944, 6914815200, 206059083120, 8700740615808, 332779651158240, 15916427365716864, 738672634596405600, 39847940942657495040, 2163098542598925281280, 130682368989193123952640
Offset: 0

Views

Author

Seiichi Manyama, Mar 15 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*(2*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+1)!));

Formula

a(n) = n! * (2*n)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (2*n-k+1)! ).

A377391 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^3 ).

Original entry on oeis.org

1, 0, 6, 9, 528, 3150, 157032, 2060100, 102770112, 2276373456, 120136435200, 3868551141840, 221493499198848, 9438561453784320, 592954244405195904, 31417910131585330080, 2173884244961012121600, 137231093173511486016000, 10452538023125775799541760
Offset: 0

Views

Author

Seiichi Manyama, Oct 27 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 3*n!*(3*n+2)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+3)!));

Formula

E.g.f. A(x) satisfies A(x) = ( 1 - x*A(x)*log(1 - x*A(x)) )^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371231.
a(n) = 3 * n! * (3*n+2)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+3)! ).

A371272 E.g.f. satisfies A(x) = 1 + x*A(x)^3 * (exp(x*A(x)^3) - 1).

Original entry on oeis.org

1, 0, 2, 3, 148, 905, 40506, 542437, 25080392, 562677201, 28058678110, 908452740701, 49777760550684, 2120072013408505, 128583516119137730, 6778703037793746165, 455574282215526201616, 28520235381763443992993, 2118889776612629769160518
Offset: 0

Views

Author

Seiichi Manyama, Mar 16 2024

Keywords

Crossrefs

Cf. A371231.

Programs

  • PARI
    a(n) = n!*(3*n)!*sum(k=0, n\2, stirling(n-k, k, 2)/((n-k)!*(3*n-k+1)!));

Formula

a(n) = n! * (3*n)! * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (3*n-k+1)! ).
Showing 1-3 of 3 results.