A145087 Row 2 of square table A145085.

1, 1, 4, 31, 373, 6250, 136711, 3740137, 124143598, 4887140221, 224203589593, 11819532185476, 707883494843341, 47708648339054629, 3589347850731252292, 299381557667730507907, 27518788652896695773041

Offset

0,3

Comments

Let S(n,x) be the e.g.f. of row n of square table A145085, then the e.g.f.s satisfy: S(n,x) = exp( Integral S(n+1,x)^(n+1) dx ) for n>=0.

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: A(x) = S(2,x) = exp( Integral S(3,x)^3 dx ) where S(n,x) is the e.g.f. of row n of square table A145085.

E.g.f.: A(x) = R(2,x)^(1/2) = exp( Integral R(3,x) dx ) where R(2,x) = e.g.f. of A145082 and R(3,x) = e.g.f. of A145083.

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]^(1/2), 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], n, x)}

Crossrefs

Cf. A145085, A145086, A145088, A145089; A145080, A145082.

Sequence in context: A266757 A369737 A198865 * A215529 A351798 A005046

Adjacent sequences: A145084 A145085 A145086 * A145088 A145089 A145090

Keyword

nonn

Author

Paul D. Hanna, Oct 01 2008

Status

approved