A101495 Column 1 of triangle A101494.

1, 1, 3, 8, 23, 73, 253, 948, 3817, 16433, 75295, 365600, 1874083, 10108025, 57194585, 338615084, 2092609701, 13470059649, 90137761867, 625940219896, 4503468629391, 33520255302185, 257764170849941, 2045255722438180

Offset: 0

Author

Paul D. Hanna, Jan 21 2005

Keywords

• nonn

Comments

a(n) is the number of m-tuples of nonnegative integers in which n-m+1 is the maximum and appears exactly once. - Mathew Englander, Apr 11 2021

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..590
• Mathew Englander, Comments on A101494 and A089246, and related sequences

Crossrefs

Cf. A101494.

Programs

GAP

List([0..30],n->Sum([0..n],k->(k+1)*(n-k)^k)); # Muniru A Asiru, Mar 05 2019

Magma

[(&+[(k+1)*(n-k)^k: k in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 05 2019

Mathematica

Join[{1},Table[Sum[(k+1)(n-k)^k,{k,0,n}],{n,30}]] (* Harvey P. Dale, Mar 04 2013 *)

PARI

a(n) = sum(k=0, n, (k+1)*(n-k)^k); \\ Michel Marcus, Mar 05 2019

Sage

[sum((k+1)*(n-k)^k for k in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 05 2019

Formula

From Vladeta Jovovic, Sep 07 2006: (Start)

a(n) = Sum_{k=0..n} (k+1)*(n-k)^k.

G.f.: Sum_{k>=0} x^k/(1-k*x)^2. (End)