A187806 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n * Product_{k=1..n+1} (1-k*x).

1, 2, 7, 39, 314, 3388, 46409, 776267, 15406059, 354928082, 9330754204, 276092552520, 9092298247070, 330151121828252, 13114259187006717, 566025800996830823, 26391137839213285415, 1322515573450223865750, 70912312814053387968103, 4052279260763983306587339

Offset: 0

Author

Paul D. Hanna, Jan 06 2013

Keywords

• nonn

Comments

Compare to: 1 = Sum_{n>=0} A082161(n)*x^n * Product_{k=1..n+1} (1-k*x).

Examples

			1/(1-x) = (1-x) + 2*x*(1-x)*(1-2*x) + 7*x^2*(1-x)*(1-2*x)*(1-3*x) + 39*x^3*(1-x)*(1-2*x)*(1-3*x)*(1-4*x) + 314*x^4*(1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x) + 3388*x^5*(1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x) +...
		

Links

• Fedor Petrov, On a generating function and vector ν of length n, answer to question on MathOverflow (2024).

Crossrefs

Cf. A082161, A118805.

Programs

PARI

{a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k*prod(j=1, k+1, 1-j*x+x*O(x^n))), n))}
for(n=0,20,print1(a(n),", "))

PARI

upto(n) = my(v1); v1 = vector(n+1, i, 1); for(i=1, n, for(j=i+1, n+1, v1[j] += i*v1[j-1])); v1 \\ Mikhail Kurkov, Oct 25 2024