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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174921 A symmetrical triangle sequence:q=4;c(n,q)=Product[(1 - q^i), {i, 1, n}]:t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q)) 0
 1, 1, 1, 1, 10, 1, 1, 325, 325, 1, 1, 6562, 123202, 6562, 1, 1, 112897, 33489370, 33489370, 112897, 1, 1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1, 1, 29746117, 2222580052225, 586055248782085, 586055248782085 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 12, 652, 136328, 67204536, 159297658162, 1176555717160856, 43519834692800379792, 5103194797279049583074896, 3003810774554741345908169533490,...}. LINKS FORMULA q=4; c(n,q)=Product[(1 - q^i), {i, 1, n}]: t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q)) EXAMPLE {1}, {1, 1}, {1, 10, 1}, {1, 325, 325, 1}, {1, 6562, 123202, 6562, 1}, {1, 112897, 33489370, 33489370, 112897, 1}, {1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1}, {1, 29746117, 2222580052225, 586055248782085, 586055248782085, 2222580052225, 29746117, 1}, {1, 476854570, 569255746164562, 2405110998912836842, 38708474182528667842, 2405110998912836842, 569255746164562, 476854570, 1}, {1, 7633866385, 145746464523607810, 9856072134501813576226, 2541741180758550820487026, 2541741180758550820487026, 9856072134501813576226, 145746464523607810, 7633866385, 1}, {1, 122160735226, 37312168908143937601, 40375323007070415995666026, 166656597689187698199553355626, 2670416828455727470616462144530, 166656597689187698199553355626, 40375323007070415995666026, 37312168908143937601, 122160735226, 1} MATHEMATICA Clear[t, n, m, c, q] c[n_, q_] = Product[(1 - q^i), {i, 1, n}] t[n_, m_, q_] = 1 + Binomial[n, m]^2 + (c[n, q]/(c[m, q]*c[n - m, q]))^2 - 2*Binomial[n, m]*c[n, q]/(c[m, q]*c[n - m, q]) Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}] CROSSREFS Sequence in context: A172378 A015124 A156767 * A010180 A109013 A213790 Adjacent sequences:  A174918 A174919 A174920 * A174922 A174923 A174924 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Apr 02 2010 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 January 23 19:12 EST 2020. Contains 331175 sequences. (Running on oeis4.)