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

0,3

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

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)

Mathematica

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

Prog

(GAP) List([0..30], n->Sum([0..n], k->(k+1)*(n-k)^k)); # Muniru A Asiru, Mar 05 2019
(PARI) a(n) = sum(k=0, n, (k+1)*(n-k)^k); \\ Michel Marcus, Mar 05 2019
(Magma) [(&+[(k+1)*(n-k)^k: k in [0..n]]): n in [0..30]]; // G. C. Greubel, 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

Crossrefs

Cf. A101494.

Sequence in context: A148777 A124462 A047857 * A134758 A050511 A151405

Adjacent sequences: A101492 A101493 A101494 * A101496 A101497 A101498

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2005

Status

approved