A275936 Shifts 6 places under binomial transform.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 463, 810, 1464, 3262, 10269, 40404, 165635, 653580, 2439069, 8626470, 29121393, 94647798, 299273206, 933818700, 2935248294, 9557815564, 33225405312, 125646127446, 514785555355, 2232901148760, 9976014439674, 44944467146100, 201608952292578, 895062795448170

Offset: 0

Author

Olivier Gérard, Aug 12 2016

Keywords

• nonn
• easy
• eigen

Links

• Robert Israel, Table of n, a(n) for n = 0..800

Crossrefs

Cf. A000998, A275934, A275935.

Programs

Maple

A:= Array(0..10000):
A[5]:= 1:
for n from 6 to 100 do
  A[n]:= add(binomial(n-6,i)*A[i],i=0..n-6);
od:
convert(A,list); # Robert Israel, Mar 04 2024

Formula

Sum_{i=0..n} binomial(n,i)*a(i) = a(n+6).

G.f. A(x) satisfies: A(x) = x^5 + x^6 * A(x/(1 - x)) / (1 - x). - Ilya Gutkovskiy, Jul 01 2021