A008785 -id:A008785 - cp's OEIS frontend

A008790 a(n) = n^(n+4).

0, 1, 64, 2187, 65536, 1953125, 60466176, 1977326743, 68719476736, 2541865828329, 100000000000000, 4177248169415651, 184884258895036416, 8650415919381337933, 426878854210636742656, 22168378200531005859375

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008789, A008791.

List([0..20], n-> n^(n+4)); # G. C. Greubel, Sep 11 2019

[n^(n+4): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

a:=n->mul(n,k=-3..n):seq(a(n),n=0..20); # Zerinvary Lajos, Jan 26 2008

Table[n^(n+4),{n,0,20}](* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

vector(20, n, (n-1)^(n+3)) \\ G. C. Greubel, Sep 11 2019

[n^(n+4) for n in (0..20)] # G. C. Greubel, Sep 11 2019

E.g.f.: T*(1 +22*T +58*T^2 +24*T^3)*(1-T)^(-9); where T is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
See A008517 and A134991 for similar e.g.f.s and diagonals of A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d^4/dx^4 {x^4/(T(x)^4*(1-T(x)))}, where T(x) = Sum_{n>=1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012

A173249 Partial sums of A000272.

Original entry on oeis.org

1, 2, 3, 6, 22, 147, 1443, 18250, 280394, 5063363, 105063363, 2463011054, 64380375278, 1856540769315, 58550453144611, 2004745521503986, 74062339559431922, 2936485391069247715, 124376016487663499491

Offset: 0

Jonathan Vos Post, Feb 13 2010

Partial sums of number of trees on n labeled nodes. The subsequence of primes in this sequence begin: 2, 58550453144611, no more through a(30).

			a(19) = 1 + 1 + 1 + 3 + 16 + 125 + 1296 + 16807 + 262144 + 4782969 + 100000000 + 2357947691 + 61917364224 + 1792160394037 + 56693912375296 + 1946195068359375 + 72057594037927936 + 2862423051509815793 + 121439531096594251776 + 5480386857784802185939.

Cf. A000055, A000169, A000312, A007778, A007830, A008785-A008791, A033842, A000272, A036361, A036362, A036506, A000055, A054581, A097170

a(n) = SUM[i=0..n] A000272(i) = SUM[i=0..n] i^(i-2).

A301270 Number of labeled trees on n vertices containing two fixed non-adjacent edges.

Original entry on oeis.org

4, 20, 144, 1372, 16384, 236196, 4000000, 77948684, 1719926784, 42417997492, 1157018619904, 34599023437500, 1125899906842624, 39618312131623748, 1499253470328324096, 60724508119499193196, 2621440000000000000000, 120167769980326767578964, 5829995856912430117421056, 298461883710362842247633948, 16079954871362414694843285504

Offset: 4

Marko Riedel, Mar 17 2018

nonn

			The edges {1,2} and {3,4} can form a tree by being joined by an edge in four ways (two possibilities for each edge).

M. Lavrov and M. Riedel, math.stackexchange.com, Number of labelled trees on n vertices containing two fixed non-adjacent edges

Cf. A000169, A000272, A008785.

Array[4 #^(# - 4) &, 21, 4] (* Michael De Vlieger, Mar 19 2018 *)

a(n) = 0 for n < 4, 4 * n^(n-4) = 4 * A008785(n-4) otherwise.

A364870 Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.

Original entry on oeis.org

1, 1, 1, 4, 2, 1, 27, 9, 3, 1, 256, 64, 16, 4, 1, 3125, 625, 125, 25, 5, 1, 46656, 7776, 1296, 216, 36, 6, 1, 823543, 117649, 16807, 2401, 343, 49, 7, 1, 16777216, 2097152, 262144, 32768, 4096, 512, 64, 8, 1, 387420489, 43046721, 4782969, 531441, 59049, 6561, 729, 81, 9, 1

Offset: 0

Stefano Spezia, Aug 11 2023

			The array begins:
     1,    1,     1,     1,     1,      1, ...
     1,    2,     3,     4,     5,      6, ...
     4,    9,    16,    25,    36,     49, ...
    27,   64,   125,   216,   343,    512, ...
   256,  625,  1296,  2401,  4096,   6561, ...
  3125, 7776, 16807, 32768, 59049, 100000, ...
  ...

Cf. A000012 (n=0), A000169, A000272, A000312 (k=0), A007830 (k=3), A008785 (k=4), A008786 (k=5), A008787 (k=6), A031973 (antidiagonal sums), A052746 (2nd superdiagonal), A052750, A062971 (main diagonal), A079901 (read by descending antidiagonals), A085527 (1st superdiagonal), A085528 (1st subdiagonal), A085532, A099753.

A[n_,k_]:=(n+k)^n; Join[{1},Table[A[n-k,k],{n,9},{k,0,n}]]//Flatten

E.g.f. of k-th column: LambertW(-x)^k/(x^k*(1 + LambertW(-x))).

cp's OEIS Frontend

A008790 a(n) = n^(n+4).

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A173249 Partial sums of A000272.

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A301270 Number of labeled trees on n vertices containing two fixed non-adjacent edges.

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A364870 Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.

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