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.

A368524 a(n) = Sum_{k=1..n} k^2 * n^(n-k).

Original entry on oeis.org

0, 1, 6, 30, 180, 1455, 15666, 213500, 3521736, 68101245, 1508916310, 37661140506, 1045012524348, 31900040161899, 1062139933257690, 38299757176168440, 1486670929792295696, 61800664096000744569, 2738952078516469743678, 128909373997071187219990
Offset: 0

Views

Author

Seiichi Manyama, Dec 28 2023

Keywords

Crossrefs

Cf. A062805, A368505, A368525.
Cf. A368526, A368534.

Programs

  • PARI
    a(n) = sum(k=1, n, k^2*n^(n-k));

Formula

a(n) = [x^n] x * (1+x)/((1-n*x) * (1-x)^3).
a(n) = n * (n+1) * (n^n - n^2 + n - 1)/(n-1)^3 for n > 1.

A368527 a(n) = Sum_{k=1..n} k^3 * n^k.

Original entry on oeis.org

0, 1, 34, 804, 18244, 434205, 11138766, 310151632, 9370253320, 306232628625, 10783859167810, 407523041660196, 16461877678462668, 708207095198943613, 32338800248010936694, 1562509380160144645440, 79657105206246202521616
Offset: 0

Views

Author

Seiichi Manyama, Dec 28 2023

Keywords

Crossrefs

Cf. A062806, A303991, A368526.
Cf. A368525.

Programs

  • PARI
    a(n) = sum(k=1, n, k^3*n^k);

Formula

a(n) = [x^n] n*x * (1+4*n*x+(n*x)^2)/((1-x) * (1-n*x)^4).
a(n) = n * (n^n * (n^6-3*n^5+8*n^3-4*n^2-7*n-1) + n^2 + 4*n + 1)/(n-1)^4 for n > 1.

A368536 a(n) = Sum_{k=1..n} binomial(k+1,2) * n^k.

Original entry on oeis.org

0, 1, 14, 192, 2996, 53955, 1110786, 25808160, 668740808, 19129643325, 598902606310, 20371538593296, 748148581865532, 29505258575474591, 1243695052515891626, 55800352470853933440, 2655106829377875895056, 133547801741230053460761
Offset: 0

Views

Author

Seiichi Manyama, Dec 29 2023

Keywords

Crossrefs

Cf. A062806, A368537.
Cf. A368526.

Programs

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

Formula

a(n) = [x^n] n*x/((1-x) * (1-n*x)^3).
a(n) = n * (n^n * (n^4-n^3-3*n^2+3*n+2) - 2)/(2 * (n-1)^3) for n > 1.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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