The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081582 Pascal-(1,7,1) array. 13
 1, 1, 1, 1, 9, 1, 1, 17, 17, 1, 1, 25, 97, 25, 1, 1, 33, 241, 241, 33, 1, 1, 41, 449, 1161, 449, 41, 1, 1, 49, 721, 3297, 3297, 721, 49, 1, 1, 57, 1057, 7161, 14721, 7161, 1057, 57, 1, 1, 65, 1457, 13265, 44961, 44961, 13265, 1457, 65, 1, 1, 73, 1921, 22121, 108353, 192969, 108353, 22121, 1921, 73, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS One of a family of Pascal-like arrays. A007318 is equivalent to the (1,0,1)-array. A008288 is equivalent to the (1,1,1)-array. Rows include A017077, A081593, A081594. Coefficients of the row polynomials in the Newton basis are given by A013614. LINKS Vincenzo Librandi, Rows n = 0..100, flattened FORMULA T(n,k) = Sum_{j = 0..n-k) binomial(n-k,j)*binomial*(k,j)*8^j. Riordan array (1/(1 - x), x*(1 + 7*x)/(1 - x)). Square array T(n, k) defined by T(n, 0) = T(0, k)=1, T(n, k) = T(n, k-1) + 7*T(n-1, k-1) + T(n-1, k). Rows are the expansions of (1 + 7*x)^k/(1 - x)^(k+1). T(n, k) = Hypergeometric2F1([-k, k-n], [1], 8). - Jean-François Alcover, May 24 2013 E.g.f. for the n-th subdiagonal, n = 0,1,2,..., equals exp(x)*P(n,x), where P(n,x) is the polynomial Sum_{k = 0..n} binomial(n,k)*(8*x)^k/k!. For example, the e.g.f. for the second subdiagonal is exp(x)*(1 + 16*x + 64*x^2/2) = 1 + 17*x + 97*x^2/2! + 241*x^3/3! + 449*x^4/4! + 721*x^5/5! + .... - Peter Bala, Mar 05 2017 Sum_{k=0..n} T(n, k) = A015519(n+1). - G. C. Greubel, May 26 2021 EXAMPLE Rows begin   1,  1,   1,    1,     1, ... A000012;   1,  9,  17,   25,    33, ... A017077;   1, 17,  97,  241,   449, ... A081593;   1, 25, 241, 1161,  3297, ...   1, 33, 449, 3297, 14721, ... Triangle begins:   1;   1,  1;   1,  9,    1;   1, 17,   17,    1;   1, 25,   97,   25,     1;   1, 33,  241,  241,    33,    1;   1, 41,  449, 1161,   449,   41,    1;   1, 49,  721, 3297,  3297,  721,   49,  1;   1, 57, 1057, 7161, 14721, 7161, 1057, 57, 1; MATHEMATICA Table[ Hypergeometric2F1[-k, k-n, 1, 8], {n, 0, 10}, {k, 0, n}]//Flatten (* Jean-François Alcover, May 24 2013 *) PROG (MAGMA) A081582:= func< n, k, q | (&+[Binomial(k, j)*Binomial(n-j, k)*q^j: j in [0..n-k]]) >; [A081582(n, k, 7): k in [0..n], n in [0..12]]; // G. C. Greubel, May 26 2021 (Sage) flatten([[hypergeometric([-k, k-n], [1], 8).simplify() for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 26 2021 CROSSREFS Cf. Pascal (1,m,1) array: A123562 (m = -3), A098593 (m = -2), A000012 (m = -1), A007318 (m = 0), A008288 (m = 1), A081577 (m = 2), A081578 (m = 3), A081579 (m = 4), A081580 (m = 5), A081581 (m = 6), A143683 (m = 8). Cf. A015519, A017077, A081593. Sequence in context: A128060 A168625 A143681 * A174346 A144404 A014761 Adjacent sequences:  A081579 A081580 A081581 * A081583 A081584 A081585 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Mar 23 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)