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.

A356962 E.g.f. satisfies log(A(x)) = x^2/2 * (exp(x*A(x)) - 1) * A(x).

Original entry on oeis.org

1, 0, 0, 3, 6, 10, 465, 3801, 20608, 461196, 7609185, 85446955, 1661943756, 38070386718, 692342989429, 15023805426735, 404978989779120, 10131679290423736, 264474729910772433, 8059571860456028835, 249785940327179846500, 7837578968934515202570
Offset: 0

Views

Author

Seiichi Manyama, Sep 06 2022

Keywords

Crossrefs

Programs

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

Formula

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

A356968 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^3/6 * A(x)).

Original entry on oeis.org

1, 0, 0, 0, 4, 10, 40, 210, 4144, 40320, 409800, 4527600, 72552480, 1170449280, 19489513680, 338983444800, 6672681818880, 141166715289600, 3149324442700800, 73497460049395200, 1825098639493104000, 47984287767342796800, 1326460667797094860800
Offset: 0

Views

Author

Seiichi Manyama, Sep 06 2022

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).

A356970 E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2 * A(x)).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 1980, 16128, 136080, 4224960, 70943040, 1087178400, 31274100000, 784834652160, 18115033128192, 565994928945600, 18161466717139200, 560655551681971200, 20108422243585658880, 769928646324249699840, 29464638272901949824000
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2022

Keywords

Crossrefs

Programs

  • Mathematica
    m = 21; (* number of terms *)
    A[_] = 0;
    Do[A[x_] = 1/(1 - x*A[x])^(x^2*A[x]) + O[x]^m // Normal, {m}];
    CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*abs(stirling(n-2*k, k, 1))/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.
Showing 1-3 of 3 results.