A226639 a(n) = n^4/8 + (5*n^3)/12 - n^2/8 - (5*n)/12 + 1.

1, 1, 1, 5, 20, 56, 126, 246, 435, 715, 1111, 1651, 2366, 3290, 4460, 5916, 7701, 9861, 12445, 15505, 19096, 23276, 28106, 33650, 39975, 47151, 55251, 64351, 74530, 85870, 98456, 112376, 127721, 144585, 163065, 183261, 205276, 229216, 255190, 283310, 313691

Offset

-1,4

Links

Table of n, a(n) for n=-1..39.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = stirling2(n+2,n)-(n+2)*stirling2(n+1,n)+((n+1)*(n+2))/2.

a(n-1) = Sum_{j=0..n} (j-1)^(n+2)*(-1)^(n-j)*binomial(n,j)/n!.

G.f.: -(6*x^2-4*x+1) / (x*(x-1)^5). - Colin Barker, Sep 06 2013

a(n) = Sum_{k=1..n+2} Sum_{i=1..k} (n-i+1)*(n-k+1). - Wesley Ivan Hurt, Sep 12 2017

Mathematica

Table[n^4/8 + (5*n^3)/12 - n^2/8 - (5*n)/12 + 1, {n, -1, 50}] (* T. D. Noe, Jun 14 2013 *)

Prog

(PARI) x='x+O('x^99); Vec(-(6*x^2-4*x+1)/(x*(x-1)^5)) \\ Altug Alkan, Sep 13 2017

Crossrefs

Sequence in context: A348310 A062988 A181936 * A264874 A270092 A272277

Adjacent sequences: A226636 A226637 A226638 * A226640 A226641 A226642

Keyword

nonn,easy

Author

Vladimir Kruchinin, Jun 13 2013

Status

approved