A182349 G.f.: exp( Sum_{n>=1} 6 * A084214(n) * x^n/n ) where g.f. of A084214 is (1+x^2)/((1+x)*(1-2*x)).

1, 6, 30, 120, 435, 1446, 4536, 13560, 39045, 108950, 296178, 787368, 2053335, 5265750, 13306380, 33188040, 81815145, 199585830, 482290630, 1155444120, 2746489851, 6481600326, 15195437280, 35407315800, 82038719565, 189089191926, 433704632346, 990244936520

Offset: 0

Author

Paul D. Hanna, Apr 25 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 6*x + 30*x^2 + 120*x^3 + 435*x^4 + 1446*x^5 + 4536*x^6 +...
such that
log(A(x))/6 = x + 4*x^2/2 + 6*x^3/3 + 14*x^4/4 + 26*x^5/5 + 54*x^6/6 + 106*x^7/7 + 214*x^8/8 +...+ A084214(n) * x^n/n +...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-6,-24,39,42,-72,-48,48,32).

Crossrefs

Cf. A084214.

Programs

Mathematica

CoefficientList[Series[1/((1+x)^4(1-2x)^5),{x,0,30}],x] (* or *) LinearRecurrence[{6,-6,-24,39,42,-72,-48,48,32},{1,6,30,120,435,1446,4536,13560,39045},30] (* Harvey P. Dale, Aug 11 2021 *)

PARI

{A084214(n)=polcoeff((1+x^2)/((1+x)*(1-2*x+x*O(x^n))), n)}
{a(n)=polcoeff(exp(sum(k=1, n, 6*A084214(k)*x^k/k)+x*O(x^n)), n)}
for(n=0, 16, print1(a(n), ", "))

Formula

G.f.: 1/((1+x)^4*(1-2*x)^5).