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A073405 Coefficient triangle of polynomials (rising powers) related to convolutions of A002605(n), n >= 0, (generalized (2,2)-Fibonacci). Companion triangle is A073406. 5
1, 36, 12, 1536, 888, 120, 80448, 62592, 15168, 1152, 5068800, 4813056, 1600704, 222336, 10944, 375598080, 413351424, 169917696, 32811264, 2992896, 103680, 32103751680, 39661608960, 19066503168, 4592982528 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The row polynomials are p(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 q(k,n) := sum(b(k,m)*n^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A073406(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*(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.

Triangle begins:

  1;

  36, 12;

  1536, 888, 120;

  ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

CROSSREFS

Cf. A002605, A073387, A073406, A073403.

Sequence in context: A109256 A277983 A066583 * A298572 A260383 A056770

Adjacent sequences:  A073402 A073403 A073404 * A073406 A073407 A073408

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)