A262002 L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^2 + 1) ).

2, 6, 28, 164, 1132, 8916, 78608, 765904, 8170752, 94755776, 1187551088, 16004096144, 230910861872, 3553052000336, 58100442762368, 1006457051734784, 18415695160624192, 354980774078690496, 7190981550797464448, 152744987909458781824, 3395058926880381635712, 78814259879097446800256

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Formula

O.g.f.: 1 - 1/G(x) where G(x) is the g.f. of A262001.

Example

L.g.f.: L(x) = 2*x + 6*x^2/2 + 28*x^3/3 + 164*x^4/4 + 1132*x^5/5 + 8916*x^6/6 + 78608*x^7/7 + 765904*x^8/8 + 8170752*x^9/9 + 94755776*x^10/10 +...
such that
exp(L(x)) = 1 + 2*x + 10*x^2/2! + 100*x^3/3! + 1700*x^4/4! + 44200*x^5/5! + 1635400*x^6/6! +...+ A101686(n)*x^n/n! +...
where A101686(n) = Product_{k=1..n} (k^2+1).
Also, given the o.g.f. A(x) = Sum_{n>=1} a(n)*x^n,
o.g.f.: A(x) = 2*x + 6*x^2 + 28*x^3 + 164*x^4 + 1132*x^5 + 8916*x^6 +...
then
1/(1 - A(x)) = 1 + 2*x + 10*x^2 + 60*x^3 + 400*x^4 + 2900*x^5 + 22700*x^6 + 191600*x^7 + 1746400*x^8 + 17230000*x^9 + 184348000*x^10 +...+ A262001(n)*x^n +...

Prog

(PARI) {a(n) = n*polcoeff( log(sum(m=0, n+1, x^m/m!*prod(k=1, m, k^2+1)) +x*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A101686, A262001.

Sequence in context: A358265 A356633 A109570 * A245633 A345367 A156626

Adjacent sequences: A261999 A262000 A262001 * A262003 A262004 A262005

Keyword

nonn

Author

Paul D. Hanna, Sep 08 2015

Status

approved