A145082 Row 2 of square table A145080.

1, 2, 10, 86, 1090, 18710, 412402, 11253638, 370191682, 14385490550, 649929193426, 33702126998438, 1984615178100514, 131531988461545238, 9736285622878908466, 799603624057192515014, 72433928850731333868034

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..16.

Formula

E.g.f.: A(x) = R(2,x) = exp( 2*Integral R(3,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)^2 where G(x) is the e.g.f. of A145087, which is row 2 of square table A145085.

Prog

(PARI) a(n)=local(A=vector(n+3, j, 1+j*x)); for(i=0, n+2, for(j=0, n, m=n+2-j; A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[2], n, x)
(PARI) a(n)=local(A=vector(n+3, j, 1+j*x)); for(i=0, n+2, for(j=0, n, m=n+2-j; A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[2]^2, n, x)
(PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n+1-k)*(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, A145083, A145084, A145085, A145087.

Sequence in context: A367372 A371005 A208833 * A335501 A355083 A295836

Adjacent sequences: A145079 A145080 A145081 * A145083 A145084 A145085

Keyword

nonn

Author

Paul D. Hanna, Oct 01 2008

Status

approved