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 A168422 Number triangle with row sums given by quadruple factorial numbers A001813. 0
 1, 1, 1, 7, 4, 1, 71, 39, 9, 1, 1001, 536, 126, 16, 1, 18089, 9545, 2270, 310, 25, 1, 398959, 208524, 49995, 7120, 645, 36, 1, 0, 10391023, 5394991, 1301139, 190435, 18445, 1197, 49, 1, 312129649, 161260336, 39066076, 5828704, 589750, 41776, 2044 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Reversal of coefficient array for the polynomials P(n,x)=sum{k=0..n, (C(n+k,2k)(2k)!/k!)*x^k*(1-x)^(n-k)}. Note that P(n,x)=sum{k=0..n, A113025(n,k)*x^k*(1-x)^(n-k)}. Row sums are A001813. LINKS FORMULA Number triangle T(n,k)=T(n,k)=(1/k!)*sum{j=0..n, (-1)^(j-k)*(2n-j)!/((n-j)!*(j-k)!)} EXAMPLE Triangle begins 1, 1, 1, 7, 4, 1, 71, 39, 9, 1, 1001, 536, 126, 16, 1, 18089, 9545, 2270, 310, 25, 1, 398959, 208524, 49995, 7120, 645, 36, 1, 10391023, 5394991, 1301139, 190435, 18445, 1197, 49, 1, 312129649, 161260336, 39066076, 5828704, 589750, 41776, 2044, 64, 1 Production matrix begins 1, 1, 6, 3, 1, 40, 20, 5, 1, 336, 168, 42, 7, 1, 3456, 1728, 432, 72, 9, 1, 42240, 21120, 5280, 880, 110, 11, 1, 599040, 299520, 74880, 12480, 1560, 156, 13, 1, 9676800, 4838400, 1209600, 201600, 25200, 2520, 210, 15, 1 Complete this with a top row (1,0,0,0,...) and invert: we get 1, -1, 1, -3, -3, 1, -5, -5, -5, 1, -7, -7, -7, -7, 1, -9, -9, -9, -9, -9, 1, -11, -11, -11, -11, -11, -11, 1, -13, -13, -13, -13, -13, -13, -13, 1, -15, -15, -15, -15, -15, -15, -15, -15, 1, -17, -17, -17, -17, -17, -17, -17, -17, -17, 1 CROSSREFS Cf. A079267. Sequence in context: A258330 A011407 A021907 * A187056 A103240 A155531 Adjacent sequences:  A168419 A168420 A168421 * A168423 A168424 A168425 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Nov 25 2009 STATUS approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)