0,3

Equals row sums of triangle A089962, which is the matrix inverse of triangle A071207.

a(n) = sum_{k=0..n} (-1)^(n-k)*C(n, k)*n*k^(n-k-1). 1 = sum_{k=0..n} C(n, k)*n^(n-k)*a(k). O.g.f.: A(x) = (1-x)*sum_{n>=0} x^n/(1+n*x)^(n+2). E.g.f.: (1-x)*exp(x*exp(-x)).

Note the diagonal of 1's in the array of iterated binomial transforms:

[1, 0, -3, 1, 17, -49, -71, 1079,..]

[1, 1, -2, -7, 4, 17, -134, 121,..]

[1, 2, 1, -9, -31, -47, -135, -599,..]

[1, 3, 6, 1, -52, -271, -1034, -3895,..]

[1, 4, 13, 29, 1, -445, -3311, -18461,..]

[1, 5, 22, 81, 212, 1, -5166, -49631,..]

[1, 6, 33, 163, 689, 2117, 1, -75019,..]

[1, 7, 46, 281, 1564, 7553, 26830, 1,..]

(PARI) a(n)=if(n<0, 0, if(n==0, 1, sum(k=0, n, (-1)^(n-k)*binomial(n, k)*n*k^(n-k-1) )))

Cf. A089962, A089981, A071207.

Sequence in context: A162313 A060281 A151918 this_sequence A143849 A105626 A071210

Adjacent sequences: A089971 A089972 A089973 this_sequence A089975 A089976 A089977

sign

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 18 2003