A251686 G.f.: exp( Sum_{n>=1} A132303(n)/3 * x^n/n ), where A132303(n) = sum of the cubes of the trinomial coefficients in row n of triangle A027907.

1, 1, 8, 100, 1556, 27260, 515510, 10284094, 213433728, 4566363088, 100082133066, 2236952393302, 50817223209451, 1170319824912699, 27268900054818390, 641812268110993694, 15239341125950643462, 364655982858022960206, 8785745372509009963892, 212976842702489760621536

Offset: 0

Author

Paul D. Hanna, Feb 28 2015

Keywords

• nonn

Comments

Self-convolution cube yields A168593.

Examples

			G.f.: A(x) = 1 + x + 8*x^2 + 100*x^3 + 1556*x^4 + 27260*x^5 +...
where
log(A(x)) = 1*x + 15*x^2/2 + 277*x^3/3 + 5727*x^4/4 + 125301*x^5/5 + 2843643*x^6/6 + 66214485*x^7/7 + 1571497119*x^8/8 +...+ A132303(n)/3*x^n/n +...
		

Crossrefs

Cf. A168593, A132303, A027907.

Programs

PARI

{A027907(n,k) = polcoeff((1+x+x^2)^n, k)}
{A132303(n) = sum(k=0, 2*n, A027907(n,k)^3)}
{a(n) = if(n==0, 1, polcoeff(exp(sum(m=1, n, A132303(m)/3 * x^m/m) +x*O(x^n)), n))}
for(n=0,30,print1(a(n),", "))