A262001 G.f.: 1/(1 - x*F'(x)/F(x)) where F(x) = Sum_{n>=0} x^n/n!*Product_{k=1..n} (k^2 + 1).

1, 2, 10, 60, 400, 2900, 22700, 191600, 1746400, 17230000, 184348000, 2140118000, 26925784000, 366118706000, 5359236310000, 84077608400000, 1407341155720000, 25027454132360000, 471046698018440000, 9351091483806800000, 195213433887227200000, 4274234604872786800000, 97924306054031604400000

Offset

0,2

Comments

Cf. A262002, which is defined by: Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^2+1) = exp( Sum_{n>=1} A262002(n)*x^n/n ).

Sum of all terms results in the 10-adic number x = ...5211383820350605156083728207423149062180073.

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: 1/(1 - G(x)) where G(x) is an o.g.f. of A262002.

a(n) == 0 (mod 10) for n>1.

Example

O.g.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 400*x^4 + 2900*x^5 + 22700*x^6 +...
where
1 - 1/A(x) =  2*x + 6*x^2 + 28*x^3 + 164*x^4 + 1132*x^5 + 8916*x^6 + 78608*x^7 + 765904*x^8 + 8170752*x^9 +...+ A262002(n)*x^n +...
Note that if we define the logarithmic series:
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 +...+ A262002(n)*x^n/n +...
then 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).

Prog

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

Crossrefs

Cf. A262002.

Sequence in context: A137571 A215002 A301625 * A276310 A098616 A082042

Adjacent sequences: A261998 A261999 A262000 * A262002 A262003 A262004

Keyword

nonn

Author

Paul D. Hanna, Sep 08 2015

Status

approved