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 A245683 Array T(n,k) read by antidiagonals, where T(0,k) = -A226158(k) and T(n+1,k) = 2*T(n,k+1) - T(n,k). 0
 0, 2, 1, 0, 1, 1, -6, -3, -1, 0, 0, -3, -3, -2, -1, 50, 25, 11, 4, 1, 0, 0, 25, 25, 18, 11, 6, 3, -854, -427, -201, -88, -35, -12, -3, 0, 0, -427, -427, -314, -201, -118, -65, -34, -17, 24930, 12465, 6019, 2796, 1241, 520, 201, 68, 17, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Take T(n,k) = -A226158(k) and its transform via T(n+1,k) = 2*T(n,k+1) - T(n,k): 0,       1,    1,    0,   -1,    0,   3,   0, -17, ... 2,       1,   -1,   -2,    1,    6,  -3, -34, ...     = A230324 0,      -3,   -3,    4,   11,  -12, -65, ... -6,     -3,   11,   18,  -35, -118, ... 0,      25,   25,  -88, -201, ... 50,     25, -201, -314, ... 0,    -427, -427, ... -854, -427, ... 0, ... Every row is alternatively an autosequence of the first kind, see A226158, and of the second kind, see A190339. The second column is twice 1, -3, 25, -427, 12465, ... = (-1)^n*A009843(n) which is in the third column. See A132049(n), numerators of Euler's formula for Pi from the Bernoulli numbers, A243963 and A245244. Hence a link between the Genocchi numbers and Pi. a(n) is the triangle of the increasing antidiagonals. LINKS EXAMPLE Triangle a(n):    0,    2,  1,    0,  1,  1,   -6, -3, -1,  0,    0, -3, -3, -2, -1,   50, 25, 11,  4,  1,  0,   etc. MATHEMATICA t[0, 0] = 0; t[0, 1] = 1; t[0, k_] := -k*EulerE[k-1, 0]; t[n_, k_] := t[n, k] = -t[n-1, k] + 2*t[n-1, k+1]; Table[t[n-k, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 04 2014 *) CROSSREFS Cf. A226158, A230324, A009843, A132049, A243963, A245244. Sequence in context: A198062 A226690 A318557 * A273712 A129634 A266825 Adjacent sequences:  A245680 A245681 A245682 * A245684 A245685 A245686 KEYWORD sign,tabl AUTHOR Paul Curtz, Jul 29 2014 STATUS approved

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Last modified July 30 12:08 EDT 2021. Contains 346359 sequences. (Running on oeis4.)