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A073406 Coefficient triangle of polynomials (rising powers) related to convolutions of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle is A073405. 3
2, 36, 12, 1056, 672, 96, 43968, 40416, 10752, 864, 2396160, 2815488, 1051776, 156672, 8064, 161879040, 226492416, 105981696, 22125312, 2121984, 76032, 13044326400, 20766633984, 11446769664, 2995605504 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The row polynomials are q(k,x) := sum(a(k,m)*x^m,m=0..k), k=0,1,2,...

The k-th convolution of U0(n) := A002605(n), n>= 0, ((2,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073387(n+k,k) = 2*(p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*U0(n))/(k!*12^k)), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A073405(k,m).

LINKS

Table of n, a(n) for n=0..24.

W. Lang, First 7 rows.

FORMULA

Recursion for row polynomials defined in the comments: p(k, n)= 2*((n+2)*p(k-1, n+1)+2*(n+2*(k+1))*p(k-1, n)+(n+3)*q(k-1, n)); q(k, n)= 4*((n+1)*p(k-1, n+1)+(n+2*(k+1))*q(k-1, n)), k >= 1.

EXAMPLE

k=2: U2(n)=2*((36+12*n)*(n+1)*U0(n+1)+(36+12*n)*(n+2)*U0(n))/(2!*12^2), cf. A073389.

2; 36,12; 1056,672,96; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

CROSSREFS

Cf. A002605, A073387, A073403-A073405.

Sequence in context: A094716 A094725 A095397 * A256060 A096513 A037418

Adjacent sequences:  A073403 A073404 A073405 * A073407 A073408 A073409

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)