A179469 G.f. satisfies A(x) = exp( Sum_{n>=1} 2^n*A(x^n)*x^n/n ).

1, 2, 8, 32, 140, 624, 2928, 14048, 69200, 347040, 1768120, 9122144, 47572128, 250341312, 1327718272, 7089595552, 38082093120, 205638343552, 1115635692576, 6078058719232, 33239328613648, 182402290944576, 1004073853702320

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

From Seiichi Manyama, Jun 02 2023: (Start)

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-2*x^(k+1))^a(k).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 2^(k/d) * a(d-1) ) * a(n-k). (End)

Example

G.f.: A(x) = 1 + 2*x + 8*x^2 + 32*x^3 + 140*x^4 + 624*x^5 + +...
log(A(x)) = 2*A(x) + 4*A(x^2)*x^2/2 + 8*A(x^3)*x^3/3 + 16*A(x^4)*x^4/4 +...

Prog

(PARI) {a(n)=my(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^m+x*O(x^n))*2^m*x^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A054598, A179470.

Sequence in context: A150848 A150849 A150850 * A150851 A150852 A150853

Adjacent sequences: A179466 A179467 A179468 * A179470 A179471 A179472

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2010

Status

approved