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.

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A368486 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * j^k.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 3, 18, 6, 1, 0, 4, 75, 90, 10, 1, 0, 5, 260, 804, 346, 15, 1, 0, 6, 805, 5444, 5988, 1146, 21, 1, 0, 7, 2310, 31180, 70980, 36363, 3450, 28, 1, 0, 8, 6279, 159774, 671180, 710980, 193827, 9722, 36, 1, 0, 9, 16392, 756420, 5468190, 10436805, 6019396, 943968, 26106, 45, 1
Offset: 0

Views

Author

Seiichi Manyama, Dec 26 2023

Keywords

Examples

			Square array begins:
  1,  0,    0,     0,      0,        0, ...
  1,  1,    2,     3,      4,        5, ...
  1,  3,   18,    75,    260,      805, ...
  1,  6,   90,   804,   5444,    31180, ...
  1, 10,  346,  5988,  70980,   671180, ...
  1, 15, 1146, 36363, 710980, 10436805, ...
		

Crossrefs

Columns k=0..3 give A000012, A000217, A036800, A343808.
Main diagonal gives A303991.

Programs

  • PARI
    T(n, k) = sum(j=0, n, k^j*j^k);

Formula

G.f. of column k: k*x*A_k(k*x)/((1-x) * (1-k*x)^(k+1)), where A_n(x) are the Eulerian polynomials for k > 0.

A368466 a(n) = Sum_{k=0..n} 2^k * k^n.

Original entry on oeis.org

1, 2, 18, 250, 4810, 118458, 3557610, 126109562, 5153959338, 238596116794, 12340467941098, 705262375055610, 44135963944338474, 3001795007526424250, 220466095716711140202, 17389850740043552754298, 1466156761178169939270826, 131580021359494993268692026
Offset: 0

Views

Author

Seiichi Manyama, Dec 25 2023

Keywords

Crossrefs

Main diagonal of A368479.

Programs

  • PARI
    a(n) = sum(k=0, n, 2^k*k^n);

Formula

a(n) ~ 2^n * n^n / (1 - exp(-1)/2). - Vaclav Kotesovec, Dec 26 2023
Showing 1-2 of 2 results.