A211194 G.f.: Sum_{n>=0} n! * (x/2)^n * Product_{k=1..n} (3*k-1) / (1 + k*(3*k-1)/2*x).

1, 1, 4, 31, 394, 7441, 195544, 6822451, 305075254, 17010802021, 1157048302084, 94291964597671, 9069435785880514, 1016607721798423801, 131360503523334458224, 19382685928544981625691, 3239003918648541605116174, 608539911518928818091672781

Offset

0,3

Comments

O.g.f. is related to pentagonal numbers A000326. If b(n) = A000326(n)*x/(1+A000326(n)x), we have A(x) = 1 +b(1) +b(1)b(2) +b(1)b(2)b(3) +b(1)b(2)b(3)b(4) + ... . Philippe Deléham, Feb 04 2013

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: Sum_{n>=0} A084939(n) * x^n / Product_{k=1..n} (1 + k*(3*k-1)/2*x).

a(n) = Sum_{k, 0<=k<=n} A211183(n,k)*3^(n-k). - Philippe Deléham, Feb 03 2013

Example

G.f.: A(x) = 1 + x + 5*x^2 + 49*x^3 + 797*x^4 + 19417*x^5 + 661829*x^6 +...
where
A(x) = 1 + 1*x/(1+x) + 1*5*x^2/((1+x)*(1+5*x)) + 1*5*12*x^3/((1+x)*(1+5*x)*(1+12*x)) + 1*5*12*22*x^4/((1+x)*(1+5*x)*(1+12*x)*(1+22*x)) + 1*5*12*22*35*x^5/((1+x)*(1+5*x)*(1+12*x)*(1+22*x)*(1+35*x)) + 1*5*12*22*35*51*x^6/((1+x)*(1+5*x)*(1+12*x)*(1+22*x)*(1+35*x)*(1+51*x)) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n, m!*(x/2)^m*prod(k=1, m, (3*k-1)/(1+(3*k-1)/2*k*x+x*O(x^n)))), n)}
for(n=0, 21, print1(a(n), ", "))

Crossrefs

Cf. A110501, A024283, A221972, A211183, A084939.

Sequence in context: A005046 A323568 A174324 * A237581 A319074 A195195

Adjacent sequences: A211191 A211192 A211193 * A211195 A211196 A211197

Keyword

nonn

Author

Paul D. Hanna, Feb 03 2013

Status

approved