0,5

Rows form the initial coefficients of powers of e.g.f. of A100065:

G100065^0: [1,__0,0,0,0,0,0,0,0,...],

G100065^1: [1,1,__3,-3,-57,369,3861,-76617,-413775,...],

G100065^2: [1,2,8,__12,-84,-12,7200,-40716,-1301328,...],

G100065^3: [1,3,15,51,__27,-513,4077,33237,-1211895,...],

G100065^4: [1,4,24,120,408,__216,-3168,45576,-202176,...],

G100065^5: [1,5,35,225,1215,4365,__1485,-27765,440865,...],

G100065^6: [1,6,48,372,2628,15084,53856,__10908,-282960,...],

G100065^7: [1,7,63,567,4851,36603,216405,777609,__93177,...],

G100065^8: [1,8,80,816,8112,74352,585792,3558672,12810240,...],...

such that for each row n, Sum_{k=0..n} T(n,k)/k! = [exp(n)]:

[exp(0)] = 1 = 1

[exp(1)] = 1+1 = 2

[exp(2)] = 1+2+8/2! = 7

[exp(3)] = 1+3+15/2!+51/3! = 20

[exp(4)] = 1+4+24/2!+120/3!+408/4! = 54

[exp(5)] = 1+5+35/2!+225/3!+1215/4!+4365/5! = 148

(PARI) {T(n, k)=if(n==0, 1, if(k==0, 1, if(k==n, n!*(floor(exp(n))-sum(j=0, n-1, T(n, j)/j!)), k!*polcoeff((Ser(vector(n, i, T(n-1, i-1)/(i-1)!), x)+x*O(x^k))^(n/(n-1)), k, x))))}

Cf. A100065.

Sequence in context: A081882 A155694 A143198 this_sequence A156029 A120026 A109089

Adjacent sequences: A100061 A100062 A100063 this_sequence A100065 A100066 A100067

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 02 2004