A145083 Row 3 of square table A145080.

1, 3, 21, 243, 4029, 88491, 2450085, 82648611, 3313381293, 154912893243, 8322387603093, 507658268093811, 34817646211022301, 2662987196578490187, 225556061819586894597, 21030571231219899162435

Offset

0,2

Comments

Let R(n,x) be the e.g.f. of row n of square table A145080, then the

e.g.f.s satisfy: R(n,x) = exp( n*Integral R(n+1,x) dx ) for n>=1.

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: A(x) = R(3,x) = exp( 3*Integral R(4,x) dx ) where R(n,x) is the e.g.f. of row n of square table A145080.

E.g.f.: A(x) = G(x)^3 where G(x) is the e.g.f. of A145088, which is row 3 of square table A145085.

Prog

(PARI) a(n)=local(A=vector(n+4, j, 1+j*x)); for(i=0, n+3, for(j=0, n, m=n+3-j; A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[3], n, x)
(PARI) a(n)=local(A=vector(n+4, j, 1+j*x)); for(i=0, n+3, for(j=0, n, m=n+3-j; A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[3]^3, n, x)
(PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n-k+2)*(A+x*O(x^n))))); n!*polcoeff(A, n)
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Jan 08 2014

Crossrefs

Cf. A145080, A145081, A145082, A145084, A145085, A145088.

Sequence in context: A234855 A367375 A058562 * A234303 A138213 A193333

Adjacent sequences: A145080 A145081 A145082 * A145084 A145085 A145086

Keyword

nonn

Author

Paul D. Hanna, Oct 01 2008

Status

approved