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A125814 q-Bell numbers for q=4; eigensequence of A022168, which is the triangle of Gaussian binomial coefficients [n,k] for q=4. 5
1, 1, 2, 8, 72, 1552, 84416, 12107584, 4726583424, 5150624868864, 16010990175691264, 144648776120641766400, 3857411545088966609514496, 307705704204270334224705015808, 74294186209325019487040708053442560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = Sum_{k=0..n-1} A022168(n-1,k) * a(k) for n>0, with a(0)=1.

EXAMPLE

The recurrence: a(n) = Sum_{k=0..n-1} A022168(n-1,k) * a(k)

is illustrated by:

a(2) = 1*(1) + 5*(1) + 1*(2) = 8;

a(3) = 1*(1) + 21*(1) + 21*(2) + 1*(8) = 72;

a(4) = 1*(1) + 85*(1) + 357*(2) + 85*(8) + 1*(72) = 1552.

Triangle A022168 begins:

1;

1, 1;

1, 5, 1;

1, 21, 21, 1;

1, 85, 357, 85, 1;

1, 341, 5797, 5797, 341, 1;

1, 1365, 93093, 376805, 93093, 1365, 1; ...

PROG

(PARI) /* q-Binomial coefficients: */ {C_q(n, k)=if(n<k || k<0, 0, if(n==0 || k==0, 1, prod(j=n-k+1, n, 1-q^j)/prod(j=1, k, 1-q^j)))} /* q-Bell numbers = eigensequence of q-binomial triangle: */ {B_q(n)=if(n==0, 1, sum(k=0, n-1, B_q(k)*C_q(n-1, k)))} /* Eigensequence at q=4: */ {a(n)=subst(B_q(n), q, 4)}

CROSSREFS

Cf. A022168, A125810, A125811, A125812, A125813, A125815.

Sequence in context: A038057 A107270 A294351 * A295044 A305000 A013002

Adjacent sequences:  A125811 A125812 A125813 * A125815 A125816 A125817

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 10 2006

STATUS

approved

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Last modified September 25 13:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)