A187806 - OEIS

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

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OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..19.

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

EXAMPLE

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) +...

PROG

(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

CROSSREFS

Cf. A082161, A118805.

Sequence in context: A322152 A368927 A336185 * A369196 A300519 A103365

Adjacent sequences: A187803 A187804 A187805 * A187807 A187808 A187809

KEYWORD

nonn,changed

AUTHOR

Paul D. Hanna, Jan 06 2013

STATUS

approved