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A194353 G.f.: exp( Sum_{n>=1} (x^n/n)/sqrt(1 - 4*x^n) ). 2
1, 1, 3, 9, 32, 114, 431, 1633, 6306, 24466, 95604, 374920, 1475731, 5822941, 23027817, 91225983, 361945480, 1437855016, 5718242653, 22762417519, 90684186378, 361540944078, 1442313708600, 5757140994990, 22991764612516, 91861397186492 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{n>=1} 1/(1-x^n)^binomial(2*n-2,n-1).

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 32*x^4 + 114*x^5 + 431*x^6 +...

where

log(A(x)) = x/sqrt(1-4*x) + (x^2/2)/sqrt(1-4*x^2) + (x^3/3)/sqrt(1-4*x^3) +...

Other expansions:

log(A(x)) = x*(1 + 2*x + 6*x^2 + 20*x^3 + 70*x^4 + 252*x^5 +...)

+ x^2/2*(1 + 2*x^2 + 6*x^4 + 20*x^6 + 70*x^8 + 252*x^10 +...)

+ x^3/3*(1 + 2*x^3 + 6*x^6 + 20*x^9 + 70*x^12 + 252*x^15 +...) +...

log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 85*x^4/4 + 351*x^5/5 + 1535*x^6/6 + 6469*x^7/7 +...

1/A(x) = (1-x)*(1-x^2)^2*(1-x^3)^6*(1-x^4)^20*(1-x^5)^70*(1-x^6)^252*...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (x^m/m)/sqrt(1-4*x^m+x*O(x^n)))), n)}

CROSSREFS

Sequence in context: A148983 A148984 A289611 * A148985 A148986 A052872

Adjacent sequences:  A194350 A194351 A194352 * A194354 A194355 A194356

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 23 2011

STATUS

approved

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)