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A073401 Coefficient triangle of polynomials (rising powers) related to convolutions of A001045(n+1), n >= 0, (generalized (1,2)-Fibonacci). Companion triangle is A073402. 3
1, 30, 9, 1050, 531, 63, 44520, 29610, 6165, 405, 2245320, 1789614, 502821, 59454, 2511, 131891760, 120133692, 41182344, 6686631, 517104, 15309, 8862693840, 8966770308, 3559509360, 714174327 (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) := A001045(n+1), n>= 0, ((1,2) Fibonacci numbers starting with U0(0)=1) with itself is Uk(n) := A073370(n+k,k) = (p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*2*U0(n))/(k!*9^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)= A073402(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)= (n+2)*p(k-1, n+1)+4*(n+2*(k+1))*p(k-1, n)+2*(n+3)*q(k-1, n); q(k, n)= (n+1)*p(k-1, n+1)+4*(n+2*(k+1))*q(k-1, n), k >= 1.

EXAMPLE

k=2: U2(n)=((30+9*n)*(n+1)*U0(n+1)+(33+9*n)*(n+2)*2*U0(n))/(2*9^2), cf. A073372.

1; 30,9; 1050,531,63; ... (lower triangular matrix a(k,m), k >= m >= 0, else 0).

CROSSREFS

Cf. A001045, A073370, A073399, A073372, A073402, A073400.

Sequence in context: A040876 A277982 A287921 * A040875 A131773 A091746

Adjacent sequences:  A073398 A073399 A073400 * A073402 A073403 A073404

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)