A323228 a(n) = binomial(n + 4, n - 1) + 1.

1, 2, 7, 22, 57, 127, 253, 463, 793, 1288, 2003, 3004, 4369, 6189, 8569, 11629, 15505, 20350, 26335, 33650, 42505, 53131, 65781, 80731, 98281, 118756, 142507, 169912, 201377, 237337, 278257, 324633, 376993, 435898, 501943, 575758, 658009, 749399, 850669

Offset: 0

Author

Peter Luschny, Feb 12 2019

Keywords

• nonn
• easy

Crossrefs

A040000 (m=1), A000027 (m=2), A000124 (m=3), A050407 (m=4), A145126 (m=5), this sequence (m=6).

Programs

Maple

aList := proc(len) local gf, ser:
gf := (x - (x - 1)^5)/(x - 1)^6:
ser := series(gf, x, len+2):
seq(coeff(ser, x, n), n=0..len) end: aList(38);

Mathematica

Table[Binomial[n + 4, n - 1] + 1, {n, 0, 37}]

Formula

a(n) = 1 + Pochhammer(n, 5)/5!.

a(n) = [x^n] (x - (x - 1)^5)/(x - 1)^6.