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
Keywords
Examples
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).
Crossrefs
Cf. A262002.
Programs
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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),", "))
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.
Comments