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.

Previous Showing 21-22 of 22 results.

A354979 Triangle read by rows. T(n, k) = |Stirling1(k + n, n)|.

Original entry on oeis.org

1, 1, 1, 1, 3, 11, 1, 6, 35, 225, 1, 10, 85, 735, 6769, 1, 15, 175, 1960, 22449, 269325, 1, 21, 322, 4536, 63273, 902055, 13339535, 1, 28, 546, 9450, 157773, 2637558, 44990231, 790943153, 1, 36, 870, 18150, 357423, 6926634, 135036473, 2681453775, 54631129553
Offset: 0

Views

Author

Peter Luschny, Jun 15 2022

Keywords

Examples

			[0] 1;
[1] 1,  1;
[2] 1,  3,  11;
[3] 1,  6,  35,   225;
[4] 1, 10,  85,   735,   6769;
[5] 1, 15, 175,  1960,  22449,  269325;
[6] 1, 21, 322,  4536,  63273,  902055,  13339535;
[7] 1, 28, 546,  9450, 157773, 2637558,  44990231,  790943153;
[8] 1, 36, 870, 18150, 357423, 6926634, 135036473, 2681453775, 54631129553;
		

Crossrefs

T(n, 1) = A000217, T(n, n) = A187646, A354980 (row sums), A132393.

A376873 a(n) = n! * |Stirling1(2*n, n)|.

Original entry on oeis.org

1, 1, 22, 1350, 162456, 32319000, 9604465200, 3986353491120, 2202727143576960, 1563325251963995520, 1385918755006365216000, 1500893038955163069216000, 1949720475921117012670233600, 2992360962617823634351113600000, 5356716752093284789859604692736000
Offset: 0

Views

Author

Peter Luschny, Oct 29 2024

Keywords

Crossrefs

Programs

  • Maple
    a := n -> n! * abs(Stirling1(2*n, n)):
    seq(a(n), n = 0..14);
  • Mathematica
    Array[#!*Abs[StirlingS1[2 #, #]] &, 14] (* Michael De Vlieger, Oct 29 2024 *)
  • PARI
    a(n) = n!*abs(stirling(2*n, n, 1)); \\ Michel Marcus, Oct 29 2024
    
  • Python
    from sympy.functions.combinatorial.numbers import factorial, stirling
    def A376873(n): return factorial(n)*stirling(n<<1,n,kind=1) # Chai Wah Wu, Oct 29 2024

Formula

a(n) = n!*A187646(n).
a(n) = A225479(2*n, n).
Previous Showing 21-22 of 22 results.