1,1

a(n)= Stirling1(n+6, n), n>=1, with Stirling1(n, k)= A008275(n, k).

E.g.f. with offset 6: exp(x)*sum(A112486(6, m)*(x^(6+m))/(6+m)!, m=0..6).

a(n)= (f(n+5, 6)/12!)*sum(A112486(6, m)*f(12, 6-m)*f(n-1, m), m=0..min(6, n-1)), with the falling factorials f(n, k):=n*(n-1)*...*(n-(k-1)). From the e.g.f.

a(n)=(binomial(n+6, 7)/r(8, 5))*sum(A112007(5, m)*r(n+7, 5-m)*f(n-1, m), m=0..5), with rising factorials r(n, k):=n*(n+1)*...*(n+(k-1)) and falling factorials f(n, m). From the g.f.

G.f.: x*(720+3708*x+4400*x^2+1452*x^3+114*x^4+x^5)/(1-x)^13. See row k=5 of triangles A112007 or A008517 for the coefficients.

(Other) sage: [stirling_number1(n, n-6) for n in xrange(7, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]

Sixth diagonal A053567.

Sequence in context: A052521 A052785 A052783 this_sequence A004033 A137891 A056271

Adjacent sequences: A111999 A112000 A112001 this_sequence A112003 A112004 A112005

nonn,easy

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005