A185310 G.f.: Sum_{n>=0} n! * (1+n*x)^n * x^n / Product_{k=1..n} (1 + k*x + n*k*x^2).

1, 1, 2, 7, 29, 154, 961, 6989, 57856, 537507, 5539661, 62713770, 773755901, 10333514049, 148523400880, 2285980425751, 37513428757945, 653836562581682, 12062552192649377, 234841212544184453, 4811561492994497360, 103490537790094623515, 2331542163236964185653

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

a(n) ~ c * d^n * n!, where d = 1.022144551255634378856..., c = 1.3357568735203273768... . - Vaclav Kotesovec, Nov 02 2014

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 29*x^4 + 154*x^5 + 961*x^6 + 6989*x^7 +...
where
A(x) = 1 + (1+x)*x/(1+x+x^2) + 2!*(1+2*x)^2*x^2/((1+x+2*x^2)*(1+2*x+4*x^2)) + 3!*(1+3*x)^3*x^3/((1+x+3*x^2)*(1+2*x+6*x^2)*(1+3*x+9*x^2)) + 4!*(1+4*x)^4*x^4/((1+x+4*x^2)*(1+2*x+8*x^2)*(1+3*x+12*x^2)*(1+4*x+16*x^2)) +...

Prog

(PARI) {a(n)=polcoeff( sum(m=0, n, m!*(1+m*x)^m*x^m*prod(k=1, m, 1/(1+k*x+m*k*x^2 +x*O(x^n))) ), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Sequence in context: A030824 A030956 A329259 * A143883 A346427 A003437

Adjacent sequences: A185307 A185308 A185309 * A185311 A185312 A185313

Keyword

nonn

Author

Paul D. Hanna, Feb 01 2013

Status

approved