A167273 Infinite product of triangle A167271 columns.

1, 1, 3, 4, 10, 13, 28, 37, 73, 97, 177, 236, 412, 548, 915, 1218, 1971, 2616, 4117, 5453, 8390, 11082, 16710, 22012, 32638, 42864, 62592, 81972, 118125, 154239, 219619, 285942, 402823, 522974, 729598, 944586, 1306233, 1686500, 2313372, 2978907, 4055968

Offset

0,3

Comments

Infinite product of triangle A167271 columns, as power series:

(1, 1, 1,...) * (1, 0, 2, 0, 3,...) * (1, 0, 0, 1, 0, 0, 1,...)

* (1, 0, 0, 3, 0, 0, 6,...) * ...

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{k>=1} Sum_{i>=0} x^(k*i)*A167271(k*(i+1), k). - Andrew Howroyd, Sep 20 2025

Prog

(PARI) T(n, k) = if(n%k==0, if(k%2, 1, binomial(n/k + k/2 - 1, k/2)))
seq(n)=Vec(prod(k=1, n, sum(i=0, n\k, x^(k*i)*T(k*(i+1), k), O(x*x^n)))) \\ Andrew Howroyd, Sep 20 2025

Crossrefs

Cf. A167271.

Sequence in context: A362649 A143372 A035594 * A392390 A096380 A309478

Adjacent sequences: A167270 A167271 A167272 * A167274 A167275 A167276

Keyword

nonn

Author

Gary W. Adamson & Mats Granvik, Oct 31 2009

Extensions

a(29) onwards from Andrew Howroyd, Sep 20 2025

Status

approved